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Let f(x) =sin^4x+cos^4x. Then f is incre...

Let `f(x) =sin^4x+cos^4x.` Then f is increasing function in the interval

A

`(pi/4,pi/2)`

B

`((5pi)/8,(3pi)/4)`

C

`(0,pi/4)`

D

`(pi/2,(5pi)/8)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=sin^4 x + cos^4 x `.Then
`f'(x) =4 sin ^3 x -4 cos^3 x sin x `
`rArr f(x) =-4 cos x sin x (cos^2 x sin x )`
`rArr f' (x)=- 2 sin 2x cos 2x =-sin 4x `
`f(x) gt 0 rArr - sin 4x 0 rArr 0`
`rArr 4x in (pi,2pi)rArr x in (pi/4,pi/2)`
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OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Section I - Solved Mcqs
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