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  • Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 15

Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 15

Answers (1)

Correct option (d)

Hint: If f(x)  is decreasing function {f}'(x)<0

Given: f(x)=2 x^{3}-9 x^{2}+12 x+29

Explanation:It is given that

f(x)=2 x^{3}-9 x^{2}+12 x+29 …..(i)

Differentiate (i) w.r.t  x

{f}'(x)=6 x^{2}-18x+12 

f(x) is decreasing {f}'(x)<0

\begin{aligned} &\Rightarrow 6 x^{2}-18 x+12<0 \\ &\Rightarrow 6\left(x^{2}-3 x+2\right)<0 \\ &\Rightarrow x^{2}-3 x+2<0 \\ &\Rightarrow(x-1)(x-2)<0 \\ &\Rightarrow 1<x<2 \end{aligned}

Thus, the function is monotonically decreasing when \begin{aligned} 1<x<2 \end{aligned}

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