Let f be continuous on the interval I = [a, b] and let c be an interior point of I. Assume that f is differentiable on (a, c) and (c, b). If there is a neighborhood (c − δ, c + δ) ⊆ I such that f ′ (x) ≤ 0 for c − δ < x < c and f ′ (x) ≥ 0 for c < x < c + δ. Prove that, f has a relative minimum at c
