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

JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Increasing and Decreasing Function

  • question_answer
     Let \[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d,0<{{b}^{2}}<c\]. Then f            [IIT Screening 2004]

    A)            Is bounded

    B)            Has a local maxima

    C)            Has a local minima

    D)            Is strictly increasing

    Correct Answer: D

    Solution :

               Given \[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d\]                    \ \[f'(x)=3{{x}^{2}}+2bx+c\]                    Now its discriminant \[=4({{b}^{2}}-3c)\]                    Þ \[4({{b}^{2}}-c)-8c<0,\] as \[{{b}^{2}}<c\] and \[c>0\]                    Therefore, \[f'(x)>0\]for all \[x\in R\]                    Hence f is strictly increasing.


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