$f(x) = (\cos x - \sin x) (17 \cos x -7 \sin x) $ $f(x) = (\cos x - \sin x) (17 \cos x -7 \sin x)$
Determine the greatest and least values of $\frac{39}{f(x)+14}$ and state a value of x at which greatest values occurs. 
Do I just use a graphing calculator for this? Is there a way I could do this without a graphing calculator?

$$f(x) = (\cos x - \sin x) (17 \cos x -7 \sin x)\\=17c^2-24sc+7s^2=7+5(1+c_2)-12s_2=12+5c_2-12s_2$$
And as we know $|as+bc|\le\sqrt{a^2+b^2}$, so:
$$-1=12-13\le f(x)\le 12+13=25$$

*$s:=\sin,c:=\cos,s_n=s(nx)$
