Let be defined for

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)=\ln\bigl(x^{2}+2x+k\bigr)

be defined for

x>0

, where

k

is a real parameter. Answer the following: (i) Find

f'(x)

. (ii) Using the expression obtained in (i), establish the condition on

k

that ensures

f'(x)>0

for every

x>0

. (iii) Hence determine the set of all real values of

k

for which

f

is strictly increasing on

(0,\infty)