Is there a simple way to find the optimum of a PolynomialFunction (which is also a UnivariateDifferentiableFunction) in commons.math? There are a bewildering array of multidimensional optimizers, but AFAICS the only explicitly univariate optimizer is Brent, which doesn't take advantage of the differentiability.
Polynomials are special functions (in the general sense of "special") and have lots of distinctive, useful properties. My advice is to exploit those properties instead of trying to use a method for more general functions. Specifically, the extreme values of a polynomial are the roots of its derivative (where the second derivative is nonzero). The derivatives of a polynomial are easy to construct and evaluate, even in Java. I see that Apache Commons Math has LaguerreSolver to find the roots of a polynomial.