Function

Derivative

Derivative[function f]

Derivative of function f(x)

Derivative[function f, number n]

n-th derivative of function f(x)

Integral

Integral[function f]

Indefinite integral for f(x)

See definte integral, 4.3.2.

Polynomial

Polynomial[function f]

yields the expanded polynomial function f.
Example: Polynomial[ (x - 3)²] yields x² - 6x + 9

TaylorPolynomial

TaylorPolynomial[function f, number a, number n]

power series expansion for function f about the point x=a to order n

Function

Function[function f, number a, number b]

yields a function, that is equal to f on the interval [a, b] and not defined outside of [a, b]