Show that , is an increasing function of x throughout its domain. A mathematical equation defining the function y = log(1+x) - (2x)/(2+x) for x > -1.

Q7 of 168 Page 205

Show that, is an increasing function of x throughout its domain.

Let y =

Now, x > -1

⇒ 1 + x >0

Also, for all x> -1,

for x > -1

Therefore, f is an increasing function throughout its domain.

Find the intervals in which the following functions are strictly increasing or decreasing:

6 – 9x – x²

Find the intervals in which the following functions are strictly increasing or decreasing:

(x + 1)³ (x – 3)³

Find the values of x for which y = [x(x – 2)]² is an increasing function.

Prove that is an increasing function of θ in