Prove that if (0) = g(0) and '(x) g'(x) for x 0, then (x) g(x) for all x 0. Show that

Prove that if ƒ(0) = g(0) and ƒ'(x) ≤ g'(x) for x ≥ 0, then ƒ(x) ≤ g(x) for all x ≥ 0. Show that the function given by y = ƒ(x) − g(x) is nonincreasing.