Let L(c) be the length of the parabola f(x) = x² from x = 0 to x = c, where c ≥ 0 is a constant.

a. Find an expression for L and graph the function.

b. Is L concave up or concave down on [0, ∞]?

c. Show that as c becomes large and positive, the arc length function increases as c²; that is, L(c) ≈ kc², where k is a constant.