Question

Let f(x)= {x^2 ; x>=0

{ax ; x<0

Find a for which f(x) is monotonically increasing function at x=0.

Answer 1

We saw that for a monotonically increasing function f’(x) ≥ 0.
For x>=0
f'(x)= 2x &
For x<0
f'(x)= a
so a must be >=0 for monotonically increasing fn at x=0