Let h = g be the product of two differentiable functions of x. a. If and

Let h = ƒg be the product of two differentiable functions of x.

a. If ƒ and g are positive, with local maxima at x = a, and if ƒ′ and g′ change sign at a, does h have a local maximum at a?

b. If the graphs of ƒ and g have inflection points at x = a, does the graph of h have an inflection point at a? In either case, if the answer is yes, give a proof. If the answer is no, give a counterexample.