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

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

Answers (1)

Answer:

a\leq 0

Given:

f(x)=x^{3}-ax

To prove:

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

Hint:

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

Solution:

Here we have

f(x)=x^{3}-ax

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.

Posted by

Gurleen Kaur

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