If $f$ and its derivatives, $f'$, $f''$, $f'''$, and so forth,
exist in an interval containing a real number $a$, we may
approximate $f(x)$ for $x$ near $a$ using a *Taylor
polynomial*. A degree-one Taylor polynomial is a tangent
line. The higher the degree, the more accurate the Taylor
approximation near $a$.

This program graphs Taylor polynomials up to order eight at an
arbitrary point, marked by a red dot. Type a function
of $x$, and press `TAB` to graph. The left and
right arrow keys move $a$. The up and down arrow keys
increase or decrease the order of approximation by one. The
less-than and greater-than keys shrink or expand the domain.

Currently graphing the Taylor polynomial: