Q58 / 90 · JEE Main 2016 (10 Apr Online) · Mathematics

Let $f (x) = \sin^{4} x + \cos^{4} x .$ Then, $f$ is an increasing function in the interval:

A
$] \frac{5 π}{8}, \frac{3 π}{4} [$
B
$] \frac{π}{2}, \frac{5 π}{8} [$
Correct answer
C
$] \frac{π}{4}, \frac{π}{2} [$
D
$] 0, \frac{π}{4} [$

Solution

$f (x) = \sin^{4} x + \cos^{4} x$

$f^{'} (x) = 4 \sin^{3} x \cos x + 4 \cos^{3} x (- \sin x)$

$= 4 \sin x \cos x (\sin^{2} x - \cos^{2} x)$

$= - 2 \sin 2 x \cos 2 x$

$= - \sin 4 x$

$f (x)$ , is increasing when $f^{'} (x) > 0$

$\Rightarrow$ $- \sin 4 x > 0$

$\Rightarrow$ $\sin 4 x < 0$

$\Rightarrow π < 4 x < 2 π$

$\Rightarrow \frac{π}{4} < x < \frac{π}{2}$
$\Rightarrow$ $x \in (\frac{π}{4}, \frac{π}{2})$

Hence, the correct answer is option: 'C'.

Let fx=sin4⁡x+cos4⁡x. Then, f is an increasing function in the interval:

Solution

Relevant Questions

Let $f (x) = \sin^{4} x + \cos^{4} x .$ Then, $f$ is an increasing function in the interval: