Calculus help?

Question

Is this true or false, and why?

If f '(c) and g '(c) are zero and h(x)= f(x) g(x), then h '(c) = 0.

Answer 1

It's true. Use the product rule:
h'(x) = f(x)g'(x) + g(x)h'(x).
Now plug c in for x:
h'(c) = 0 + 0 = 0.

Answer 2

It's true. You can think of f'(c) as the slope of f(x) at c. The slope is zero. So if h(x) is the two graphs combined and they each have zero slope at c, then h(x) has zero slope at c.