1) Recall that in class we introduced the cubic B ezier curve defined by the control points (x1, y1), (x2, y2), (x3, y3), and (x4, y4) and given parametrically for 0 t 1 by x = x1(1 t)^3 + 3 x2 t(1 t)^2 + 3 x3 t^2(1 t) + x4 t^3

y = y1(1 t)^3 + 3 y2 t(1 t)^2 + 3 y3 t^2(1 t) + y4 t^3

Prove the following facts.

a) The point (x, y) = (x1, y1) is attained when t = 0. b) The point (x, y) = (x4, y4) is attained when t = 1. c) Consider the line tangent to the curve at t = 0. Prove that the point (x, y) = (x2, y2) lies on this line. d) Consider the line tangent to the curve at t = 1. Prove that the point (x, y) = (x3, y3) lies on this line.