Back when we first looked at the derivative function graphically, we saw that the outputs of the derivative function are slopes (of tangent lines) on the graph of the original function (that the derivative is derived from). Now, we want to do the reverse. Given a derivative function, how can we uncover the function from which it is derived? [br][br]An [b]antiderivative [/b]of a function f(x) is a function F(x) whose derivative is f(x), that is, [math]F'(x)=f(x)[/math].

The graph of a function f(x) is given on the left. Use the input box to change this function. As you use the slider tool to move a point along the graph of f(x), a point and tangent line are shown on the right. The height of the graph of f(x) represents the slope of the tangent line on the graph on the right. [br][list][*]Click "Trace Antiderivative" and move the slider tool for c to trace out a graph of an antiderivative of f. Notice that f is providing a slope to use to "tell" the antiderivative which direction to go to plot the next point. [/*][*]Adjust the slider tool for C to adjust the starting point for the antiderivative graph. Re-trace the antiderivative for different values of C. [/*][*]Use the checkbox for F to show/hide the antiderivative graph, a formula for the antiderivative F(x), and the initial value which is related to C. [/*][/list]