Q4 of 292 Page 549

Prove that the function is strictly increasing on R.

Domain of the function is R

finding derivative i.e f’(x)=2e^x

As we know e^x is strictly increasing its domain

f’(x)>0

hence f(x) is strictly increasing in its domain

Show the function is a strictly decreasing function on R.

Prove that , where a and b are constants and a > 0, is a strictly increasing function on R.

Show that the function is

a. strictly increasing on [0, ∞[

b. strictly decreasing on [0, ∞[

c. neither strictly increasing nor strictly decreasing on R

Show that the function is

a. strictly increasing on ]0, ∞[

b. strictly decreasing on] − ∞, 0[