Question

Find the greatest maximum y-value of the following equation:

Answer 1

A quick way to do this is by recalling the fact that $-1\le\cos x\le1$, so the largest value that $\cos ax$ alone (for any real value of $a$) can take on is 1.

This means $-3\le3\cos2x\le3$, and so $1\le3\cos2x+4\le7$.

So the maximum value of this function is 7.