[kmundnic]

I agree that saying that he used calculus is a bit of a stretch. However, calculus is essential for all the gradient-based methods (or algorithms) in optimization. Moreover, if you want to analyze these algorithms, you have to know about convex analysis.

I think what the author _meant_ was that he used the intuition derived from calculus to tackle the problem he was framing as a mathematical optimization problem.

Also, you're right, he missed that the global maximum might not be unique in a non-concave function.