Section 1.5 Optimization
Another interesting generalization from Calculus in \(\RR^n\) is the principle of optimization. To optimize a real-valued, twice differentiable function in \(\RR^n\text{,}\) we simply look at the gradient \(\nabla f\) and find its zeroes. Then we study the Hessian matrix \(Hess f(x)\) and decide if the critical points are local maxima or minima. The analogy for functions on Banach spaces is called the Calculus of Variations, which we cover in Chapter[cross-reference to target(s) "c-variations" missing or not unique].