JEE Main & Advanced Mathematics Applications of Derivatives Question Bank

done Increasing and Decreasing Function Total Questions - 68

• question_answer1)
  The function \[x+\frac{1}{x},(x\ne 0)\]is a non-increasing function in the interval
  A)
             [? 1, 1] done clear
  B)
             [0, 1] done clear
  C)
             [?1, 0] done clear
  D)
             [?1,2] done clear
  View Solution play_arrow

• question_answer2)
  The function \[\frac{1}{1+{{x}^{2}}}\]is decreasing in the interval
  A)
             \[(-\infty ,\,-1]\] done clear
  B)
             \[(-\infty ,\,0]\] done clear
  C)
             \[[1,\infty )\] done clear
  D)
             \[(0,\infty )\] done clear
  View Solution play_arrow

• question_answer3)
  Which of the following is not a decreasing function on the interval \[\left( 0,\frac{\pi }{2} \right)\]
  A)
             \[\cos x\] done clear
  B)
             \[\cos 2x\] done clear
  C)
             \[\cos 3x\] done clear
  D)
             \[\cot x\] done clear
  View Solution play_arrow

• question_answer4)
  The function \[\frac{x-2}{x+1},(x\ne -1)\]is increasing on the interval
  A)
             \[(-\infty ,\,\,\,0]\] done clear
  B)
             [0, \[\infty \]) done clear
  C)
             R done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  In the interval [0, 1], the function \[{{x}^{2}}-x+1\]is
  A)
             Increasing                              done clear
  B)
             Decreasing done clear
  C)
             Neither increasing nor decreasing done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  The interval in which the function \[{{x}^{2}}{{e}^{-x}}\]is non decreasing, is
  A)
             \[(-\infty ,\,\,2]\] done clear
  B)
             [0, 2] done clear
  C)
             \[[2,\,\,\infty )\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer7)
  On the interval \[\left( 0,\frac{\pi }{2} \right)\], the function log sin x is
  A)
             Increasing                              done clear
  B)
             Decreasing done clear
  C)
             Neither increasing nor decreasing done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer8)
  The function \[\sin x-\cos x\]is increasing in the interval
  A)
             \[\left[ \frac{3\pi }{4},\frac{7\pi }{4} \right]\] done clear
  B)
             \[\left[ 0,\frac{3\pi }{4} \right)\] done clear
  C)
             \[\left[ \frac{\pi }{4},\frac{3\pi }{4} \right]\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer9)
  The function \[\sin x-bx+c\]will be increasing in the interval \[(-\infty ,\,\,\infty )\], if
  A)
             \[b\le 1\] done clear
  B)
             \[b\le 0\] done clear
  C)
             \[b<-1\] done clear
  D)
             \[b\ge 0\] done clear
  View Solution play_arrow

• question_answer10)
  The function \[{{x}^{4}}-4x\]is decreasing in the interval
  A)
             [?1, 1] done clear
  B)
             \[(-\infty ,\,\,1)\] done clear
  C)
             \[[1,\,\,+\infty )\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  For which interval the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\] is decreasing     [MP PET 1993]
  A)
             \[(-2,\,\infty )\] done clear
  B)
             \[(-2,\,-1)\] done clear
  C)
             \[(-\infty ,\,-1)\] done clear
  D)
             \[(-\infty ,\,\,-2)\]and \[(-1,\,\infty )\] done clear
  View Solution play_arrow

• question_answer12)
  \[f(x)={{x}^{3}}-27x+5\]is an increasing function, when                    [MP PET 1995]
  A)
             \[x<-3\] done clear
  B)
             \[|x|\,>3\] done clear
  C)
             \[x\le -3\] done clear
  D)
             \[|x|\,<3\] done clear
  View Solution play_arrow

• question_answer13)
  The function \[f(x)={{x}^{2}}\]is increasing in the interval
  A)
             \[(-1,\,1)\] done clear
  B)
             \[(-\infty ,\,\infty )\] done clear
  C)
             \[(0,\,\infty )\] done clear
  D)
             \[(-\infty ,\,0)\] done clear
  View Solution play_arrow

• question_answer14)
  Function \[f(x)={{x}^{4}}-\frac{{{x}^{3}}}{3}\]is
  A)
             Increasing for \[x>\,\frac{1}{4}\]and decreasing for \[x<\frac{1}{4}\] done clear
  B)
             Increasing for every value of x done clear
  C)
             Decreasing for every value of x done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer15)
  For every value of x function \[f(x)={{e}^{x}}\]is
  A)
             Decreasing                             done clear
  B)
             Increasing done clear
  C)
             Neither increasing nor decreasing done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer16)
  If \[f'(x)\]is zero in the interval (a, b) then in this interval it is
  A)
             Increasing function            done clear
  B)
             Decreasing function done clear
  C)
             Only for a > 0 and b>0 is increasing function done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer17)
  For the every value of x the function \[f(x)=\frac{1}{{{5}^{x}}}\]is 
  A)
             Decreasing            done clear
  B)
             Increasing done clear
  C)
             Neither increasing nor decreasing done clear
  D)
             Increasing for x > 0 and decreasing for x < 0 done clear
  View Solution play_arrow

• question_answer18)
  The interval for which the given function \[f(x)=2{{x}^{3}}-3{{x}^{2}}-36x+7\] is decreasing, is
  A)
             (? 2, 3) done clear
  B)
             (2, 3) done clear
  C)
             (2,? 3) done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer19)
  If \[f(x)=\sin x-\frac{x}{2}\] is increasing function, then  [MP PET 1987]
  A)
             \[0<x<\frac{\pi }{3}\] done clear
  B)
             \[-\frac{\pi }{3}<x<0\] done clear
  C)
             \[-\frac{\pi }{3}<x<\frac{\pi }{3}\] done clear
  D)
             \[x=\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer20)
  If x tends 0 to \[\pi \], then the given function \[f(x)=x\sin x+\cos x+{{\cos }^{2}}x\] is
  A)
             Increasing                              done clear
  B)
             Decreasing done clear
  C)
             Neither increasing nor decreasing done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer21)
  Let \[y={{x}^{2}}{{e}^{-x}}\], then the interval in which y increases with respect to x is [MNR 1994; Kurukshetra CEE 1998]
  A)
             \[(-\infty ,\infty )\] done clear
  B)
             \[(-2,\,0)\] done clear
  C)
             \[(2,\infty )\] done clear
  D)
             \[(0,\,2)\] done clear
  View Solution play_arrow

• question_answer22)
  The function \[y=2{{x}^{3}}-9{{x}^{2}}+12x-6\] is monotonic decreasing, when                                  [MP PET 1994]
  A)
             \[1<x<2\] done clear
  B)
             \[x>2\] done clear
  C)
             \[x<1\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer23)
  For which value of x, the function \[f(x)={{x}^{2}}-2x\] is decreasing                                      [BIT Ranchi 1990]
  A)
             \[x>1\] done clear
  B)
             \[x>2\] done clear
  C)
             \[x<1\] done clear
  D)
             \[x<2\] done clear
  View Solution play_arrow

• question_answer24)
  The function \[f(x)=\cos x-2px\] is monotonically decreasing for                 [RPET  1987; MP PET 2002]
  A)
             \[p<\frac{1}{2}\] done clear
  B)
             \[p>\frac{1}{2}\] done clear
  C)
             \[p<2\] done clear
  D)
             \[p>2\] done clear
  View Solution play_arrow

• question_answer25)
  If \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\]is monotonically increasing in each interval, then [RPET 1992; Kurukshetra CEE 2002]
  A)
             \[k<3\] done clear
  B)
             \[k\le 3\] done clear
  C)
             \[k>3\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer26)
  In which interval is the given function \[f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+1\] is monotonically decreasing  [RPET 1995]
  A)
             [2, 3] done clear
  B)
             (2, 3) done clear
  C)
             \[(-\infty ,\,2)\] done clear
  D)
             \[(3,\,\infty )\] done clear
  View Solution play_arrow

• question_answer27)
  The function \[f(x)=\tan x-x\] [MNR 1995; Pb. CET 2000; Karnataka CET 2002]
  A)
             Always increases                 done clear
  B)
             Always decreases done clear
  C)
             Never decreases                 done clear
  D)
             Sometimes increases and sometimes decreases done clear
  View Solution play_arrow

• question_answer28)
  The function \[f(x)=\log (1+x)-\frac{2x}{2+x}\]is increasing on                                                               [EAMCET 2002]
  A)
             (0, \[\infty \]) done clear
  B)
             (\[-\infty \], 0) done clear
  C)
             \[(-\infty ,\infty )\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer29)
  If the function \[f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}\]is increasing for all values of x, then
  A)
             \[K<1\] done clear
  B)
             \[K>1\]                                    done clear
  C)
             \[K<2\] done clear
  D)
             \[K>2\] done clear
  View Solution play_arrow

• question_answer30)
  The value of ?a? in order that \[f(x)=\sqrt{3}\] \[\sin x-\cos x-2ax+b\] decreases for all real values of x, is given by
  A)
             \[a<1\] done clear
  B)
             \[a\ge 1\] done clear
  C)
             \[a\ge \sqrt{2}\] done clear
  D)
             \[a<\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer31)
  The interval in which the function \[{{x}^{3}}\]increases less rapidly than\[6{{x}^{2}}+15x+5\], is
  A)
             \[(-\infty ,\,-1)\] done clear
  B)
             (?5 , 1) done clear
  C)
             (?1 ,5) done clear
  D)
             (5 , \[\infty \]) done clear
  View Solution play_arrow

• question_answer32)
  The values of ?a? for which the function \[(a+2){{x}^{3}}-3a{{x}^{2}}+9ax-1\] decreases monotonically throughout for all real x, are  [Kurukshetra CEE 2002]
  A)
             \[a<-2\] done clear
  B)
             \[a>-2\] done clear
  C)
             \[-3<a<0\] done clear
  D)
             \[-\infty <a\le -3\] done clear
  View Solution play_arrow

• question_answer33)
  If \[f(x)=2x+{{\cot }^{-1}}x+\log (\sqrt{1+{{x}^{2}}}-x)\], then \[f(x)\]
  A)
             Increases in [0 ,\[\infty \])      done clear
  B)
             Decreases in [0 ,\[\infty \]) done clear
  C)
             Neither increases nor decreases in (0, \[\infty \]) done clear
  D)
             Increases in (?\[\infty \],\[\infty \]) done clear
  View Solution play_arrow

• question_answer34)
  For all real values of x, increasing function f(x) is [MP PET 1996]
  A)
             \[{{x}^{-1}}\] done clear
  B)
             \[{{x}^{2}}\] done clear
  C)
             \[{{x}^{3}}\] done clear
  D)
             \[{{x}^{4}}\] done clear
  View Solution play_arrow

• question_answer35)
  The least value of k for which the function \[{{x}^{2}}+kx+1\]is an increasing function in the interval \[1<x<2\]is
  A)
             ? 4 done clear
  B)
             ? 3 done clear
  C)
             ? 1 done clear
  D)
             ? 2 done clear
  View Solution play_arrow

• question_answer36)
  The interval of the decreasing function \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\]is
  A)
             \[\left( \frac{1}{3},\,1 \right)\] done clear
  B)
   \[\left( -\frac{1}{3},1 \right)\] done clear
  C)
             \[\left( -\frac{1}{3},\,\frac{1}{3} \right)\] done clear
  D)
    \[\left( -1,-\frac{1}{3} \right)\] done clear
  View Solution play_arrow

• question_answer37)
  The function \[f(x)={{x}^{3}}-3{{x}^{2}}-24x+5\] is an increasing function in the interval given below [MP PET 1998]
  A)
             \[(-\infty ,\,-2)\cup (4,\infty )\] done clear
  B)
             \[(-2,\infty )\] done clear
  C)
              (?2, 4) done clear
  D)
             \[(-\infty ,\,4)\] done clear
  View Solution play_arrow

• question_answer38)
  Which one is the correct statement about the function \[f(x)=\sin 2x\]
  A)
             \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{2} \right)\] and decreasing in \[\left( \frac{\pi }{2},\pi  \right)\] done clear
  B)
             \[f(x)\] is decreasing in \[\left( 0,\frac{\pi }{2} \right)\] and increasing in \[\left( \frac{\pi }{2},\pi  \right)\] done clear
  C)
             \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{4} \right)\] and decreasing in \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\] done clear
  D)
             The statements ,  and  are all correct done clear
  View Solution play_arrow

• question_answer39)
  The function f defined by \[f(x)=(x+2){{e}^{-x}}\] is [IIT Screening 1994]
  A)
             Decreasing for all x             done clear
  B)
             Decreasing in \[(-\infty ,\,-1)\] and increasing in \[(-1,\infty )\] done clear
  C)
             Increasing for all x done clear
  D)
             Decreasing in \[(-1,\,\infty )\] and increasing in \[(-\infty ,\,-1)\] done clear
  View Solution play_arrow

• question_answer40)
  If \[f(x)={{x}^{3}}-10{{x}^{2}}+200x-10\], then [Kurukshetra  CEE 1998]
  A)
             \[f(x)\]is decreasing in \[]-\infty ,10]\] and increasing in \[[10,\,\infty [\] done clear
  B)
             \[f(x)\]is increasing in \[]-\infty ,10]\] and decreasing in \[[10,\,\infty [\] done clear
  C)
             \[f(x)\]is increasing throughout real line done clear
  D)
             \[f(x)\]is decreasing throughout real line done clear
  View Solution play_arrow

• question_answer41)
  If \[f(x)=\frac{x}{\sin x}\]and \[g(x)=\frac{x}{\tan x}\], where \[0<x\le 1\], then in this interval                                  [IIT 1997 Re-Exam]
  A)
             Both \[f(x)\] and \[g(x)\] are increasing functions done clear
  B)
             Both \[f(x)\] and  \[g(x)\] are decreasing functions done clear
  C)
             \[f(x)\]is an increasing function done clear
  D)
             \[g(x)\] is an increasing function done clear
  View Solution play_arrow

• question_answer42)
  Function \[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+29\] is monotonically decreasing, when  [RPET 1996]
  A)
             \[x<2\] done clear
  B)
             x > 2 done clear
  C)
             x >1 done clear
  D)
             1< x < 2 done clear
  View Solution play_arrow

• question_answer43)
  \[2{{x}^{3}}+18{{x}^{2}}-96x+45=0\]is an increasing function when                                                               [RPET 1997]
  A)
             \[x\le -8,\,x\ge 2\] done clear
  B)
             \[x<-2,x\ge 8\] done clear
  C)
             \[x\le -2,x\ge 8\] done clear
  D)
             \[0\le x\le -2\] done clear
  View Solution play_arrow

• question_answer44)
  The function \[\frac{a\sin x+b\cos x}{c\sin x+d\,\cos x}\] is decreasing, if  [RPET 1999]
  A)
             \[ad-bc>0\] done clear
  B)
             \[ad-bc<0\] done clear
  C)
             \[ab-cd>0\] done clear
  D)
             \[ab-cd<0\] done clear
  View Solution play_arrow

• question_answer45)
  The function \[f(x)=1-{{e}^{-{{x}^{2}}/2}}\] is                                     [AMU 1999]
  A)
             Decreasing for all x             done clear
  B)
             Increasing for all x done clear
  C)
             Decreasing for \[x<0\] and increasing for \[x>0\] done clear
  D)
             Increasing for \[x<0\] and decreasing for \[x>0\] done clear
  View Solution play_arrow

• question_answer46)
  Consider the following statements S and R S : Both \[\sin x\] and cosx are decreasing functions in \[\left( \frac{\pi }{2},\pi  \right)\] R : If a differentiable function decreases in (a, b)  then its derivative also decreases in (a, b). Which of the following is true [IIT Screening 2000]
  A)
             Both S and R are wrong    done clear
  B)
             Both S and R are correct but R is not the correct explanation for S done clear
  C)
             S is correct and R is the correct explanation for S      done clear
  D)
             S is correct and R is wrong done clear
  View Solution play_arrow

• question_answer47)
  The function which is neither decreasing nor increasing in \[\left( \frac{\pi }{2},\frac{3\pi }{2} \right)\] is [MP PET 2000]
  A)
             cosec x done clear
  B)
             \[\tan x\] done clear
  C)
             \[{{x}^{2}}\] done clear
  D)
             \[|x-1|\] done clear
  View Solution play_arrow

• question_answer48)
  Function \[f(x)=\frac{\lambda \sin x+6\cos x}{2\sin x+3\cos x}\] is monotonic increasing, if                             [MP PET 2001]
  A)
             \[\lambda >1\] done clear
  B)
             \[\lambda <1\] done clear
  C)
             \[\lambda <4\] done clear
  D)
             \[\lambda >4\] done clear
  View Solution play_arrow

• question_answer49)
  On the interval (1,3), the function \[f(x)=3x+\frac{2}{x}\]is                                                               [AMU 1999]
  A)
             Strictly decreasing              done clear
  B)
             Strictly increasing done clear
  C)
             Decreasing in (2, 3) only done clear
  D)
             Neither increasing nor decreasing done clear
  View Solution play_arrow

• question_answer50)
  If \[f(x)=\sin x-\cos x,\] the function decreasing in \[0\le x\le 2\pi \] is                                                    [UPSEAT 2001]
  A)
             \[[5\pi /6,\,3\pi /4]\] done clear
  B)
             \[[\pi /4,\,\pi /2]\] done clear
  C)
             \[[3\pi /2,\,5\pi /2]\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer51)
  The function \[f(x)=\frac{\log x}{x}\] is increasing in the interval                                                               [UPSEAT 2001]
  A)
             \[(1,\,2e)\] done clear
  B)
             (0,e) done clear
  C)
             (2, 2e) done clear
  D)
             (1/e, 2e) done clear
  View Solution play_arrow

• question_answer52)
  If \[f(x)=x{{e}^{x(1-x)}}\], then \[f(x)\] is                                             [IIT Screening 2001]
  A)
             Increasing on \[\left[ -\frac{1}{2},\,1 \right]\] done clear
  B)
             Decreasing on R done clear
  C)
             Increasing on R done clear
  D)
             Decreasing on \[\left[ -\frac{1}{2},1 \right]\] done clear
  View Solution play_arrow

• question_answer53)
  If \[f(x)={{x}^{3}}-6{{x}^{2}}+9x+3\] be a decreasing function, then x lies in [RPET 2002]
  A)
             \[(-\infty ,-1)\cap (3,\,\infty )\] done clear
  B)
             \[(1,\,\,3)\] done clear
  C)
             \[(3,\,\,\infty )\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer54)
  If \[f(x)=\frac{1}{x+1}-\log \,(1+x),\,x>0,\]then \[f\]is  [RPET 2002]
  A)
             An increasing function      done clear
  B)
             A decreasing function done clear
  C)
             Both increasing and decreasing function done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer55)
  The function                                                                                     \[f(x)=x\,+\,\cos x\]  is       [DCE 2002]
  A)
             Always increasing done clear
  B)
             Always decreasing done clear
  C)
             Increasing for certain range of x done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer56)
  The function                                                                                      \[f(x)={{x}^{1/x}}\] is                                                          [AMU 2002]
  A)
             Increasing in                                                                                        \[(1,\,\,\infty )\]            done clear
  B)
             Decreasing in                                                                                        \[(1,\,\,\infty )\] done clear
  C)
             Increasing in                                                                                              \[(1,\,e),\]  decreasing in                                                                                            \[(e,\infty )\] done clear
  D)
             Decreasing in                                                                                              \[(1,\,e),\]  increasing in                                                                                            \[(e,\infty )\] done clear
  View Solution play_arrow

• question_answer57)
  The function                                                                            \[f(x)=1-{{x}^{3}}-{{x}^{5}}\]  is decreasing for  [Kerala (Engg.) 2002]
  A)
             \[1\le x\le 5\] done clear
  B)
             \[x\le 1\] done clear
  C)
             \[x\ge 1\] done clear
  D)
             All values of x done clear
  View Solution play_arrow

• question_answer58)
  The function \[{{x}^{x}}\] is increasing, when   [MP PET 2003]
  A)
             \[x>\frac{1}{e}\] done clear
  B)
             \[x<\frac{1}{e}\] done clear
  C)
             \[x<0\] done clear
  D)
             For all real x done clear
  View Solution play_arrow

• question_answer59)
  \[2{{x}^{3}}-6x+5\] is an increasing function if [UPSEAT 2003]
  A)
             \[0<x<1\] done clear
  B)
             \[-1<x<1\] done clear
  C)
             \[x<-1\] or \[x>1\] done clear
  D)
             \[-1<x<-1/2\] done clear
  View Solution play_arrow

• question_answer60)
  The length of the longest interval, in which the function \[3\sin x-4\sin x\] is increasing, is                            [IIT Screening 2002]
  A)
             \[\frac{\pi }{3}\] done clear
  B)
             \[\frac{\pi }{2}\] done clear
  C)
             \[\frac{3\pi }{2}\] done clear
  D)
             \[\pi \] done clear
  View Solution play_arrow

• question_answer61)
   Let \[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d,0<{{b}^{2}}<c\]. Then f            [IIT Screening 2004]
  A)
             Is bounded done clear
  B)
             Has a local maxima done clear
  C)
             Has a local minima done clear
  D)
             Is strictly increasing done clear
  View Solution play_arrow

• question_answer62)
  If \[f(x)=x,-1\le x\le 1\], then function \[f(x)\] is                                                                               [SCRA 1996]
  A)
             Increasing done clear
  B)
             Decreasing done clear
  C)
             Stationary done clear
  D)
             Discontinuous done clear
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• question_answer63)
  For all \[x\in (0,\,1)\] [IIT Screening 2000]
  A)
             \[{{e}^{x}}<1+x\] done clear
  B)
             \[{{\log }_{e}}(1+x)<x\] done clear
  C)
             \[\sin x>x\] done clear
  D)
             \[{{\log }_{e}}x>x\] done clear
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• question_answer64)
  The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174\] is increasing in the interval [J & K 2005]
  A)
             \[\frac{1}{2}<x<1\] done clear
  B)
             \[\frac{1}{2}<x<2\] done clear
  C)
             \[3<x<\frac{59}{4}\] done clear
  D)
             \[-\infty <x<\infty \] done clear
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• question_answer65)
  The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always an increasing function on the interval                         [Kerala (Engg.) 2005]
  A)
             \[(0,\,\pi )\] done clear
  B)
             \[(0,\,\pi /2)\] done clear
  C)
             \[(0,\pi /4)\] done clear
  D)
             \[(0,\,3\pi /4)\] done clear
  E)
             \[(0,\,5\pi /4)\] done clear
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• question_answer66)
  Given function \[f(x)=\left( \frac{{{e}^{2x}}-1}{{{e}^{2x}}+1} \right)\] is [Orissa JEE 2005]
  A)
             Increasing done clear
  B)
             Decreasing done clear
  C)
             Even done clear
  D)
             None of these done clear
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• question_answer67)
  Function \[f(x)=\frac{4{{x}^{2}}+1}{x}\] is decreasing for interval
  A)
             \[\left( \frac{-1}{2},\,\frac{1}{2} \right)\] done clear
  B)
             \[\left[ \frac{1}{2},\,-\frac{1}{2} \right]\] done clear
  C)
             (? 1, 1) done clear
  D)
             [1, ?1] done clear
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• question_answer68)
  A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? [AIEEE 2005]   
  A)
                Interval                                        Function             \[\left( -\infty ,\,\frac{1}{3} \right]\]                                                   \[3{{x}^{2}}-2x+1\] done clear
  B)
              (? ¥, ? 4]                                         \[{{x}^{3}}+6{{x}^{2}}+6\] done clear
  C)
              (? ¥, ¥)                                           \[{{x}^{3}}-3{{x}^{2}}+3x+3\] done clear
  D)
                  [2, ¥)                                           \[2{{x}^{3}}-3{{x}^{2}}-12x+6\] done clear
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