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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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