Mathematics - Application of Derivative Question with Solution | TestHub

Expansion of determinant

$f\left(x\right)=\mathrm{cos }2x+\mathrm{cos }4x$

$f^{\text{'}}\left(x\right)= -2\sin 2x-4\text{sin }4x=-2\text{sin }2x\left(1+4\cos 2x\right)$

$\therefore$    maxima at $x=0$

$f^{\text{'}}\left(x\right)=0 \Rightarrow $ \text{sin}2x=0\therefore x=0\text{,}\frac{\pi }{2}\text{,}-\frac{\pi }{2}$$
and $\cos 2x= -\frac{1}{4}$ has 4 solutions in $\left(-\pi \text{,}\pi \right)$

$\therefore {\text{f}}^{ \prime }\left(x\right)=0$has more than three solutions