2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Applications of Derivatives

JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Self Evaluation Test - Application of Derivatives

  • question_answer
    Let \[f'(x)<0\] and \[g'(x)>0\] for all real x, then

    A) \[f(g(x+1))>f(g(x+5))\]

    B) \[f(g(x))<f(g(f(x+2))\]

    C) \[g(f(x))<g(f(x+2))\]

    D) \[g(f(x))>g(f(x-2))\]

    Correct Answer: A

    Solution :

    [a] Given, \[f'(x)<0\] and \[g'(x)>0\] therefore g(x) is an increasing function and f?(x) is a decreasing function \[\therefore x+1<x+5\Rightarrow g(x+1)<g(x+5)\] \[\Rightarrow f(g(x+1))>f(g(x+5))\] Again \[x<x+1\Rightarrow g(x+1)\Rightarrow f(g(x))\]                                     \[>f(g(x+1))\] \[x<x+2\Rightarrow f(x)>f(x+2)\Rightarrow g(f(x))\]                                     \[>g(f(x+1))\] \[x>x-2\Rightarrow f(x)<f(x-2)\Rightarrow g(f(x))\]                                     \[<g(f(x-2))\]


You need to login to perform this action.
You will be redirected in 3 sec spinner