Chain Rule for the Derivative of the Composition of Functions With what we have seen so far, we already have all the basics to compute almost any derivative. However, we must distinguish between the possibility of computing a derivative and the effort we invest in carrying out such calculations, and...
Weierstrass Extreme Value Theorem Why is it that in so many optimization problems it is almost taken for granted that “the maximum exists” or that “there is always a minimum” on a given interval, when in reality nothing forces that to be the case? The Weierstrass Theorem is the missing...
Maximum and Minimum Values of a Function Where is the “best” point of a function: the maximum you want to achieve or the minimum you need to avoid? That question, which arises in optimization, physics, economics, and engineering, is one of the main applications of differential calculus. And here is...
