Question

Show that the function f(x) = x² is

a. strictly increasing on [0, ∞]

b. strictly decreasing on [0, ∞]

c. neither strictly increasing nor strictly decreasing on R

Answer 1

Domain of function is R.

f’(x) = 2x

for x>0 f’(x)>0 i.e. increasing

for x<0 f’(x)<0 i.e. decreasing

hence it is neither increasing nor decreasing in R