Consider the cubic polynomial

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

f(x)=x^{3}-3kx^{2}+9x+5

, where

k\in\mathbb R

. (i) Find

f'(x)

. (ii) Determine the condition on

k

that makes

f'(x)

positive for every real

x

. (iii) Using the result obtained in (ii), find the set of real values of

k

for which the function

f

is strictly increasing on

(-\infty,\infty)