Extrema of $f(x)=\frac{\sin (5x)} 5 - \frac{2\sin(3x)} {3} + \sin (x)$. (a) I need help in finding maxima and minima of the following funcion:
$$f(x)=\frac{\sin (5x)} 5 - \frac{2\sin(3x)} {3} + \sin (x)$$
therefore I need to find the roots of $f'(x)=\cos(5x)-2\cos(3x)+\cos(x)$.
(b) I need to find the minima of $$f(x)=4x+\frac{9\pi^2} x + \sin x.$$
How can I find the roots of $$f'(x)=4-\frac{9\pi^2 }{x^2} + \cos x?$$
Thank you.

$$\begin{align}
\cos5x-2\cos3x+\cos x&=\cos5x-\cos 3x + \cos x-\cos 3x\\
&=-2\sin4x\sin x+2\sin2x\sin x\\
&=2\sin x(-\sin 4x+\sin2x)\\
&=-4\sin x\sin3x\cos x
\end{align}$$
Now you only have to equal $0$ to each factor.
