Let f and g be functions that are continuous on [a, b] and differentiable on (a, b). Show that there exists at least one point c (a, b) such that: [f(b) f(a)] g(c) = [g(b) g(a)] f(c). State explicitly every theorem you use in your proof, and why it is applicable. Hint: define a new function h(x) = f(x) g(x) on [a, b] for suitable constants and .