Question

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

f(x) = 3cos 2x + 4

Please, could you walk me through how to do this? I'd appreciate it, thanks!

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.