Approximating tangent slope with a secant slope

Calculus consists of those problems in mathematics that can be solved with the following basic approach:
Approximate and take a limit!
The simplest, standard, geometric example of this process is the approximation of the slope of a tangent line with a secant line. Here's an illustration of this basic idea.
Choose $f$: $f(x)=x^2$ $f(x)=\frac{1}{3}e^x$ $f(x)=\sin(2x^2)+x/4$
Show secant line
$h = $
secant slope =
tangent slope =

Note that the slope of the secant line is computed via the difference quotient: $$ \frac{f(x+h)-f(x)}{h} $$ and the slope of the tangent line is computed via the derivative: $$ f'(x) = \lim_{h\to0} \frac{f(x+h)-f(x)}{h}. $$