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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 1

  • question_answer
    The function \[f\left( x \right)=5+36x+3{{x}^{2}}-2{{x}^{3}}\] is decreasing in the interval

    A)  (-2,3)               

    B)  (2,-3)

    C)  (-2,-3)              

    D)  (2,3)

    Correct Answer: A

    Solution :

    [a]: Given,\[f(x)=5+36x+3{{x}^{2}}-2{{x}^{3}}\] \[\Rightarrow \]\[f'(x)=36+6x-6{{x}^{2}}=6(6+x-{{x}^{2}})\] For increasing or decreasing,\[f'(x)=0\] \[\Rightarrow 6+x-{{x}^{2}}=0\Rightarrow {{x}^{2}}-x-6=0\] \[\Rightarrow (x-3)(x+2)=0\Rightarrow x=3,-2\] \[-\infty <x<-2,f'(x)=(-ve)(-ve)=(+ve)\],Increasing \[-2<x<3,f'(x)=(-ve)(+ve)=(-ve)\], Decreasing \[3<x<\infty ,f'(x)=(+ve)(+ve)=(+ve)\], Increasing \[\therefore \]The interval in which f(x) is decreasing is (-2, 3).


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