Question

How do I make a graph of

f'(-1) = f'(1) = 0, f'(x) > 0 on (-1,1),
f'(x) < 0 for x < -1, f'(x) > 0 for x >1

Thanks.

if the derivative is postive on -1 to 1, you have a curve that shope upward as x increases.
If the derivative is zero at -1, and 1, thekn at -1 the curve is a local min, and at 1, the curve is a local max.
For x<-1, the function decreases for increasing x (or as x becomes greater negative, the curve goes upward).
For x>1, the curve again goes upward. A neat point at x=1. As the curve approaches 1 from the left, it levels off, then as x increases, it starts back up again, as a stairstep.