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The function f(x)=sin^4x +cos ^4 x incre...

The function `f(x)=sin^4x +cos ^4 x increases` if

A

It is monotonic increasing `forall` x in R.

B

f(x) fails to exist for three disticnt real values of x

C

f(x) changes its sign twice as x varifes from `-oo to oo`

D

The function attains its extreme values at `x_(1) and x_(2)` such that `x_(1)x_(2)gt0`

Text Solution

Verified by Experts

The correct Answer is:
3
Function is increasing in `(-oo,-2)cup(0,oo)` and decreasing in (-2,0)

x=-2 is local maxima and x =0 is local minima
It is dervitable `forall x in R -{ 0,1}` and continous `forall x in R `
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