jee-main 2016 Q82

jee-main · India · 10apr Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

Let $f ( x ) = \sin ^ { 4 } x + \cos ^ { 4 } x$. Then, $f$ is an increasing function in the interval:
(1) $]\frac { 5 \pi } { 8 } , \frac { 3 \pi } { 4 } [$
(2) $]\frac { \pi } { 2 } , \frac { 5 \pi } { 8 } [$
(3) $]\frac { \pi } { 4 } , \frac { \pi } { 2 } [$
(4) $]0 , \frac { \pi } { 4 } [$

Let $f ( x ) = \sin ^ { 4 } x + \cos ^ { 4 } x$. Then, $f$ is an increasing function in the interval:\\
(1) $]\frac { 5 \pi } { 8 } , \frac { 3 \pi } { 4 } [$\\
(2) $]\frac { \pi } { 2 } , \frac { 5 \pi } { 8 } [$\\
(3) $]\frac { \pi } { 4 } , \frac { \pi } { 2 } [$\\
(4) $]0 , \frac { \pi } { 4 } [$

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