Question#$4($Curve modeling techniques$)-20$ points

a$)$ What is the degree of a Bezier curve that is defined by the control points $P_0(3,2),P_1(1,4),P_2(3,5),P_3(3,5),P_4(5,4),$ and $P_5(5,2)?$

b$)$ Derive the blending functions

c$)$ Find the points on the curve which correspond: $1)u=0$; $2)u=0\mathrm{.}5$; $3)u=1$

d$)$ Sketch the curve.

e$)$ Find the tangent at $P_5$ in two different ways:

i$)$ Using the derivatives of blending functions

ii$)$ Using one of the special properties of Bezier curves.