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

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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