Let be given by

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

h_k:(0,\infty)\to\mathbb{R}

be given by

h_k(x)=\dfrac{k}{x}+x

, where

k

is a real parameter. (i) Find

h_k'(x)

. (ii) Determine the set of all

k

for which

h_k

is strictly increasing on

(0,\infty)

. (iii) Determine the set of all

k

for which

h_k

is strictly decreasing on

(0,\infty)