We've been given an extra credit problem seemingly associated with this derived variation of the Z equation.

\(R=sqrt {(Z)^2 - {(X_{C})}^2}\)

The question is as follows:

What value of R will give maximum value of Vc & Vr?

It's extra credit so I'm having trouble getting things setup to solve -- a stretch. I can't seem to understand how I would determine the maximum of Vc & Vr.

Would the max be? \(sqrt {(V_{C})^2 + ({V_{R}})^2\)

Can anyone offer a suggestion to get me pointed in the right direction, please?

Thanks!