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Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 14

Answers (1)

Correct option (d)

Hint: If f(x)  is monotonically increasing function{f}'(x)\geq 0

Given: f(x)=x^{3}-27x+5

Explanation: It is given that

f(x)=x^{3}-27x+5          …..(i)

Differentiate (i) w.r.t  x

\begin{aligned} &f^{\prime}(x)=3 x^{2}-27 \\ &f^{\prime}(x)=3\left(x^{2}-9\right) \end{aligned}

\because f(x) is increasing  {f}'(x)\geq 0

\begin{aligned} &\Rightarrow 3\left(x^{2}-9\right) \geq 0 \\ &\Rightarrow x^{2}-9 \geq 0 \\ &\Rightarrow x^{2} \geq 9 \\ &\Rightarrow|x| \geq 3 \end{aligned} 

Thus,f(x)  is increasing when \left | x \right |\geq 3

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