Relationships between first and second derivatives

Homework Statement

Figure 4.46 shows the second derivative of h(x) for -2 $$\leq$$ x $$\leq$$ 1

a) Explain why h'(x) is never negative on this interval.
b) Explain why h(x) has a global maximum at x=1
c) Sketch a possible graph of h(x) for this interval.

I realize this is probably a fairly simple question, however it's just making my head hurt.

D H
Staff Emeritus
Are you sure you have given us all of the data? Perhaps the value of h'(x) at x=-1?

sorry, don't know how i could have missed that

h'(-1)=0
h(-1)=2

D H
Staff Emeritus
For $x\ge -1$, the graph shows that h"(x) is positive. That means h'(x) is increasing. And since h'(-1)= 0 ....