For each of the following functions, find the coordinates of the stationary points and determine their nature. Sketch the curve.

a) y = x² − 8x + 12

b) y = x² − x³ 

c) y = 4x³ − x⁴

d) y = x² − 2x + 7

e) y = x³(x − 2)  

f)  y = 20 + 15x − x² − x³/3