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

a) y = x² − 2x + 5

b) y = 3 + x − x²

c) y = 2x² + 4x − 3

d) y = x³ −5x² + 3x + 1

e) y = x² − 2x² − 2

f) y = 9 + 24x − 2x³