Let be differentiable at every value of x and suppose that (1) = 1, that

Let ƒ be differentiable at every value of x and suppose that ƒ(1) = 1, that ƒ′ < 0 on (-∞, 1), and that ƒ′ > 0 on (1, ∞).

a. Show that ƒ(x) ≥ 1 for all x.

b. Must ƒ′(1) = 0? Explain.