Q7 of 292 Page 549

Prove that the function is strictly increasing on ]0, ∞[.

f(x)=ln(x)


for x<0


f’(x)=-ve →increasing


for x>0


f’(x)=+ve →decreasing


f(x) in increasing when x>0 i.e x∈(0,∞ )


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5

Show that the function is

a. strictly increasing on [0, ∞[


b. strictly decreasing on [0, ∞[


c. neither strictly increasing nor strictly decreasing on R


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Show that the function is

a. strictly increasing on ]0, ∞[


b. strictly decreasing on] − ∞, 0[


 8

Prove that the function is strictly increasing on ]0, ∞[ when a > 1 and strictly decreasing on ]0, ∞[ when 0 < a < 1.

 9

Prove that is strictly increasing on R.