f'(0)=0 f(0) = -1,

The gradient at x=0 is zero.

f'(2)=0

at x=2, the gradient is zero.

f'(x)<0 for x<2.

The gradient is less than zero for any value strictly less than x=2.

f'(x)<0 for x>2

The gradient is less than zero for any value strictly greater than x=2.

f'(x)>0 for 0<x<2.

The gradient is greater than zero for any values between (0, 2).

This seems to be a very disjointed graph.