“Look out there, Lenny. Ain’t those hills and valleys pretty?”

“Yeah George. Can we get a place over there when we get some money? Can we?”

George squinted. “Exactly where are you looking Lenny?”

Lenny pointed. “Right over there George. That local minimum.”

The calculus of multivariable functions is a straightforward generalization of single-variable calculus. Instead of a function of a single variable *t*, consider a function of several variables. To illustrate, let’s call the variables *x*, *y*, *z*, although these don’t have to stand for the coordinates of ordinary space. Moreover, there can be more or fewer then three. Let us also consider a function of these variables, *V*(*x*, *y*, *z*). For every ...

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