Suppose that f: [0, 1] → R is increasing and continuously differentiable on [0, 1]. Let T be the right triangle whose vertices are (0, f(0)), (1, f(0)), and (1, /(l)). If c represents the hypotenuse of T, a and b represent the legs of T, and L represents the arc length of the explicit curve y = f(x), x ∈ [0, 1], prove that c < L < a + b.