See attached for the problem and attemped solution, its is not an applied problem, just a theoretical problem.
Okay, so far so good.
But you just sort of stopped. Is there a particular question that you had?
You've already found the derivative of the denominator. Set the derivative equal to 0 and solve for r. You'll find that there are two or three values of r that make the derivative go to 0, but not all of them are necessarily local minimums (there could be local maximums).
Once you find the appropriate expression for r that makes the denominator a minimum, plug that back into |H(jω)| and simplify.