Suppose f is differentiable on (-∞, ∞) and assume it has a local extreme value at the point x = 2, where f(2) = 0. Let g(x) = xf(x) + 1 and let h(x) = xf(x) + x + 1, for all values of x.

a. Evaluate g(2), h(2), g'(2), and h'(2).

b. Does either g or h have a local extreme value at x = 2? Explain.