A method for maximizing the distance from the spectrum of an analytic, symmetric matrix with distinct eigenvalues from a given frequency is proposed. The method models the classical approach from optimization of finding the first derivative of the function to be maximized and setting it equal to zero. The function to be maximized is the norm of a resolvent in terms of the given perturbed matrix and the applied frequency. The problem of the function being nonsmooth is considered, and a solution is proposed. This solution entails using the concept of the generalized gradient. This method provides an efficient means for targeting the potential troublespots for resonance and avoiding them with relative ease.