#### Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 4 maths

f(x) is increasing in interval R.

Given:

$f(x)=e^{2x}$

To find:

We have to show that f(x) is increasing R.

Hint:

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

Solution:

We have

$f(x)=e^{2x}$

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

\begin{aligned} &f^{\prime}(x)=\frac{d}{d x}\left(e^{2 x}\right) \\ &f^{\prime}(x)=2 e^{2 x} \end{aligned}

For f(x) to be increasing, we must have

\begin{aligned} &\Rightarrow f^{\prime}(x)>0 \\ &\Rightarrow 2 e^{2 x}>0 \\ &\Rightarrow e^{2 x}>0 \end{aligned}

Since the value of e lies between 2 and 3.

So, whatever be the power of e (i.e, x is domain R) will greater than zero.

Hence f(x) is increase in interval R.