The document provides instructions to find the stationary points and determine their nature for various polynomial functions including f(x) = 3x^2 - 12x + 5, f(x) = -x^2 - 4x + 8, and f(x) = 2x^2 - 4, as well as several other polynomial functions involving higher degree terms and multiple roots. Students are asked to analyze where the derivatives of each function are equal to 0 or undefined to find the coordinates of stationary points and then determine whether they are maxima, minima or points of inflection.

1. Applications of Differentiation of Polynomials: Stationary Points
Find the coordinates of the stationary points of each of the following functions and determine
their nature:
a f(x) = 3x2 − 12x + 5
b f(x) = −x2 − 4x + 8
c f(x) = 2x2 − 4
d f(x) = −3x2 + 6x + 4
e f(x) = 4x3 + 6x2 − 72x + 48
f f(x) = 2x3 − 21x2 + 60x +20
g f(x) = x3 − 6x2 + 12x − 3
h f(x) = x3 + 12x2 + 48x
i f(x) = − x2 (x− 3)
j f(x) = (x − 1)2 (x − 4)
k f(x) = +x
l f(x) = x4 + 32x − 20
m f(x) = + 2x − 3
n f(x) = f(x) =