**Polynomials and Calculus**

One important aspect of calculus is the project of analyzing complicated functions by means of approximating them with polynomial functions. The culmination of these efforts is Taylor's theorem, which roughly states that every differentiable function locally looks like a polynomial function, and the Stone-Weierstrass theorem, which states that every continuous function defined on a compact interval of the real axis can be approximated on the whole interval as closely as desired by a polynomial function. Polynomial functions are also frequently used to interpolate functions.

Calculating derivatives and integrals of polynomial functions is particularly simple. For the polynomial function

the derivative with respect to *x* is

and the indefinite integral is

Read more about this topic: Polynomial

### Famous quotes containing the word calculus:

“I try to make a rough music, a dance of the mind, a *calculus* of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”

—Judith Johnson Sherwin (b. 1936)