Question

Show that the function given by f(x) = e^2 x is strictly increasing on R.

Answer 1

we know any function y = f(x) in interval [a,b] is said to be strictly increasing only when f'(x) > 0 in [a,b].

given, $\bf{f(x)=e^{2x}}$
differentiate f(x) with respect to x,
$\bf{\frac{df(x)}{dx}=f'(x)=\frac{d(e^{2x})}{dx}}\\\bf{f'(x)=2.e^{2x}}$

we get f'(x) = 2.e^{2x} ,but when we any value of x , we get f'(x) > 0 [ it is because exponential function is non negative function]
hence, it is clear that f(x) is strictly increasing function.

Answer 2

Answer:

Heya mate ,

Plz refer to the attachment for ur answer ☺

Hope it helps