a) Find an equation of a line that is tangent to the curve f(x)=2cos3x and whose slope is a maximum.

b) Is this the only possible solution? Explain. If there are other possible solutions, how many solutions are there?

For a.. I know how to find the tangent of a curve at x=something.. but this question asks to find the tangent whose slope is a maximum; what would I have to do to determine that?