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

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

Solution:

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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