JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q72

MathematicsSingle correct+4 / -1Question 72 of 90

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

\left]0,\dfrac\pi4\right[

\left]\dfrac\pi4,\dfrac\pi2\right[

\left]\dfrac\pi2,\dfrac{5\pi}8\right[

\left]\dfrac{5\pi}8,\dfrac{3\pi}4\right[

Answer and worked solution

Official answer: B

$f=1-\frac12\sin^22x=\frac34+\frac14\cos4x$ , so $f'=-\sin4x>0$ when $4x\in(\pi,2\pi)$ : $x\in\left(\frac\pi4,\frac\pi2\right)$ .

JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 72