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Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 35

Answers (1)


a\leq 0



To prove:

We have to find the value of a for which f(x) is an increasing function on R.


Given f(x) is increasing function that means f’(x) > 0.


Here we have


On differentiating both sides w.r.t x we get

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}\left(x^{3}-a x\right) \\ &\Rightarrow f^{\prime}(x)=3 x^{2}-a \end{aligned}

Given f(x) is increasing function on R

\begin{aligned} &\Rightarrow f^{\prime}(x)>0 \text { for all } x \in R\\ &\Rightarrow 3 x^{2}-a>0 \text { for all } x \in R\\ &\Rightarrow a<3 x^{2} \text { for all } x \in R\\ &\text { But the least value of } 3 x^{2}=0 \text { for } x=0 \end{aligned}

Hence a ≤ 0 is required value of a.

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Gurleen Kaur

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