$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?

HINT:
$$f(x)=17\cos^2x+7\sin^2x-24\sin x\cos x=\dfrac{17(1+\cos2x)+7(1-\cos2x)-24\sin2x}2$$
$$=12+5\cos2x-12\sin2x=12+\sqrt{12^2+5^2}\cos\left(2x+\arctan\dfrac{12}5\right)$$
Now for real $x,-1\le\cos\left(2x+\arctan\dfrac{12}5\right)\le1$
