Please give me solution of this question 

Asked by riyamjumdar22 | 6th Aug, 2019, 09:42: PM

Expert Answer:

f left parenthesis x right parenthesis equals cos squared x plus fraction numerator s e c x over denominator 4 end fraction
f apostrophe left parenthesis x right parenthesis equals negative 2 space cos x space sin x plus fraction numerator s e c x space tan x over denominator 4 end fraction
T a k e space f apostrophe left parenthesis x right parenthesis equals 0
rightwards double arrow negative 2 space cos x space sin x plus fraction numerator s e c x space tan x over denominator 4 end fraction equals 0
rightwards double arrow fraction numerator s e c x space tan x over denominator 4 end fraction equals 2 space cos x space sin x
rightwards double arrow fraction numerator sin x over denominator 4 cos squared x end fraction equals 2 space cos x space sin x
rightwards double arrow open parentheses 2 cos x close parentheses cubed equals 1
rightwards double arrow 2 cos x equals 1
rightwards double arrow cos x equals 1 half
rightwards double arrow x equals plus-or-minus straight pi over 3
N o w comma space f apostrophe left parenthesis x right parenthesis equals negative 2 cos 2 x plus 1 fourth open parentheses s e c cubed x plus tan squared x space s e c x close parentheses
f apostrophe apostrophe open parentheses straight pi over 3 close parentheses greater than 0 space
T h e r e f o r e space x equals straight pi over 3 space i s space t h e space m i n i m a
T h e r e f o r e comma space m i n i m u m space v a l u e space o f space f space i s space a t space straight pi over 3
f open parentheses straight pi over 3 close parentheses equals cos squared open parentheses straight pi over 3 close parentheses plus fraction numerator s e c begin display style straight pi over 3 end style over denominator 4 end fraction equals 1 fourth plus 2 over 4 equals 3 over 4 equals m
H e n c e comma space 8 over 3 m equals 8 over 3 cross times 3 over 4 equals 2

Answered by Renu Varma | 7th Aug, 2019, 10:11: AM

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