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