Question

Minimum positive integral value of ' $k$ ' for which $f(x)=k\cos 2x-4{\cos }^{3}x$ has exactly one critical point in $(0,\pi )$, is

Answer 1

Answer: 3

$f^{\prime }(x)=-2k\sin 2x+12{\cos }^{2}x\sin x$
$=2\sin 2x(-k+3\cos x)$
For $k\ge 3,x=\frac{\pi }{2}$ is the only critical point in $(0,\pi )$