[list][*]Use the input boxes for f(x) and a and b to define the function and its domain. [/*][*]Use the input box and slider tool for c to move c across the domain of f. [/*][*]Use the slider tool for h to adjust how far apart the two points are that are being used to calculate average rates of change. [/*][*]Use the Plot Slope checkbox to graph the slope of the secant line as a function.[/*][*]Use the Trace [math]\Delta y[/math] and Trace Slope buttons to leave traces of these objects on the graph. [/*][/list]

The difference quotient is the expression used to calculate an average rate of change over progressively smaller intervals in order to estimate the instantaneous rate of change. [br][br][math]DQ=\frac{f(c+h)-f(c)}{h}[/math][br][br]This expression calculates an average rate of change. However, if we repeat the calculation for smaller and smaller values of h (i.e., let h \to 0), then we get the instantaneous rate of change, called the derivative: [br][br][math]f'(c)=\lim_{h\to0}\frac{f(c+h)-f(c)}{h}[/math]