CUET Preparation Today
The value of C which satisfies Rolle's Theorem for $f(x)=\sin ^4 x+\cos ^4 x$ in $\left[0, \frac{\pi}{2}\right]$. Then C is: |
$\frac{\pi}{5}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ $\frac{\pi}{6}$ |
$\frac{\pi}{4}$ |
The correct answer is Option (3) - $\frac{\pi}{4}$ $f'(x)=\sin^3 x+\cos x-4\cos^3x\sin x=0$ $⇒\sin^2x=\cos^2x$ for $x=\frac{\pi}{4}$ as $x∈[0,\frac{\pi}{2}]$ |
