1.

Prove that the function f given by f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi).

Answer»

Solution :f(x) = log cos x
` rArrf'(x) = (-SIN x)/(cos x) =- tan x`
(a) For STRICTLY decreasing FUNCTION
`f'(x) LT 0`
` rArr-tan x lt 0`
` rArrtan xgt 0`
` rArr x in ]0,PI/2[`
(b) Forstrictly decreasing function
` f'(x) gt 0`
` rArr- tan x gt 0`
` rArrtan x lt 0`
` rArrx in ]pi/2, pi [`


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