Engineering How Can I Find the H-infinity Norm of a Transfer Function?

[billtodd]

Homework Statement

below

Relevant Equations

below

I want to find $\|G\|_\infty$, the solution in the pic uses the Bode plot. But to tell you the truth I am worse at drawing it.
So basically what I thought is I want to find: $|G(i\omega)|=1/\sqrt{(25−\omega^2)^2+9\omega^2}$.
So basically I much prefer to find the minimum value of what is in the sqrt from highschool calculus methods (differentiating and equating to zero).
I found something of the sort of 24.21 in the denominator, which is close to 25 but far from 15.
Am I correct in my reasoning?

 

[billtodd]

never mind I get the max is at 1/14.30908802. I had some really bad error.