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  • Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 39 subquestion (i)

Provide solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 39 subquestion (i)

Answers (1)

Answer:

 f(x)=x |x| is an increasing function for all real values.

Given:

  f(x)=x |x|

To prove:

 We have to find the interval in which f(x) is an increasing or decreasing.

Hint:

 For f(x) to be increasing function we must have f’(x) > 0.

Solution:

Here we have

f(x)=f(x)=x|x|, x \in R

We know that

f(x)=\left\{-x^{2}, \quad \text { if } x<0 \& x^{2}, \quad \text { if } x>0\right.

On differentiating f(x) w.r.t x we get

\begin{aligned} &f^{\prime}(x)=\{-2 x, \quad \text { if } x<0 \& 2 x, \quad \text { if } x>0 \\ &\Rightarrow f^{\prime}(x)>0 \text { for all value of } x . \end{aligned}

Hence f(x) is increasing function for all value of real values.

Posted by

Gurleen Kaur

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