Let (x) = (sin x)/x for x 0 and (0) = 1. (a) Plot on [3, 3]. (b) Show that (c) = 0

Let ƒ(x) = (sin x)/x for x ≠ 0 and ƒ(0) = 1.
(a) Plot ƒ on [−3π, 3π].
(b) Show that ƒ(c) = 0 if c = tan c. Use the numerical root finder on a computer algebra system to find a good approximation to the smallest positive value c₀ such that ƒ'(c₀) = 0.
(c) Verify that the horizontal line y = ƒ(c₀) is tangent to the graph of y = ƒ(x) at x = c₀ by plotting them on the same set of axes.