Mathematics

Problem

Let

f(x)=\ln(x^{2}+ax+5)

be defined on the interval

(0,\infty)

, where

a

is a real parameter. (a) Compute

f'(x)

. (b) Show that

f

is strictly increasing on

(0,\infty)

precisely when the numerator of

f'(x)

is positive for all

x>0

. (c) Find the range of

a

that satisfies the condition obtained in part (b), and hence obtain the values of

a

for which

f

is strictly increasing on its domain.