Some of us forgot the chain rule for part (d). You need to write down U = 1/2 C v^2 = 1/(2C) q^2.

So dU/dt = 1/(2C) * 2 * q * dq/dt

where q = CV cos(ωt).

Then the key is that the function f(x) = 2 sin(x) cos(x) has a max value of 1, so its coefficient is the max value of the function dU/dt.