Let f(x) = sin4x + cos4x. Then f is an increasing function in the interval :

Question

Let f(x) = sin4x + cos4x. Then f is an increasing function in the interval : (A) ] 0 , (π/4)[ (B) ] (π/4) , (π/2)[ (C) ] (π/2) , (5 π/8)[ (D) ] (5 π/8) , (3π/4)[

Tardigrade Admin · Accepted Answer

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>0 ⇒ sin 4 x<0 ⇒ π< 4 x< 2 π (π/4)< x< (π/2)

Q. Let $f (x) = s i n^{4} x + co s^{4} x$ . Then $f$ is an increasing function in the interval :

$] 0, \frac{π}{4} [$

$] \frac{π}{4}, \frac{π}{2} [$

$] \frac{π}{2}, \frac{5 π}{8} [$

$] \frac{5 π}{8}, \frac{3 π}{4} [$

$f (x) = sin^{4} x + cos^{4} x$
$f^{'} (x) = 4 sin^{3} x cos x - 4 cos^{3} x sin x$
$= 4 sin x cos x (sin^{2} x - cos^{2} x)$
$= - 2 sin 2 x . cos 2 x$
$= - sin 4 x > 0$
$\Rightarrow sin 4 x < 0$
$\Rightarrow π < 4 x < 2 π$
$\frac{π}{4} < x < \frac{π}{2}$

Q. Let f(x)=sin4x+cos4x. Then f is an increasing function in the interval :

]0,4π​[

]4π​,2π​[

]2π​,85π​[

]85π​,43π​[