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Explain solution rd sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 31

Answers (1)

[-2,-1] , Correct option (b)

Hints: Take a derivative of given equation

Given: The interval on which f(x)=2 x^{3}+9 x^{2}+12 x-1 is decreasing, is


We have,

               f(x)=2 x^{3}+9 x^{2}+12 x-1

               \begin{aligned} f^{\prime}(x) &=6 x^{2}+18 x+12 \\ &=6\left(x^{2}+3 x+2\right) \\ &=6(x+2)(x+1) \end{aligned}

              f(x) decreases when \begin{aligned} f^{\prime}(x) \leq 0 \end{aligned}


               ∴ f’(x) =                                                                           

         From the sign scheme \begin{aligned} f^{\prime}(x) \leq 0 \end{aligned}

               When \begin{aligned} x\epsilon \left [ -2,-1 \right ] \end{aligned}

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