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:
Answer & explanation
Correct answer: option 3
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 $x∈[0,\frac{\pi}{2}]$