You have determined the -coordinate of the maximum correctly, but notice your equation has two solutions ...
I'm trying to find the local maximum and minimum values for the equation but I seem to keep coming up with the wrong answer.
My working goes like this (in radians):
Local maximums and minimums appear where the gradient is 0, so:
Therefore there is a local maximum at
What I can't work out is how to find the local minimum in the same range. I think that, because local maximums and minimums are radians apart on the Cosine graph, they will be radians apart on the graph of Cos 2x, which would put the minimum point at but the book I'm working from puts it at .