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

  • question_answer
    The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174\] is increasing in the interval [J & K 2005]

    A)            \[\frac{1}{2}<x<1\]

    B)            \[\frac{1}{2}<x<2\]

    C)            \[3<x<\frac{59}{4}\]

    D)            \[-\infty <x<\infty \]

    Correct Answer: D

    Solution :

               \[{f}'\,(x)=6\,({{x}^{2}}-x+15)>0\,\forall \,x\].


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