The Derivative as a Function
- Chris Heeren
The black graph is that of the function f(x) = 1 / 3 x³ - 2 x² + 3 x + 1. Click the play button to move point (c,0) on the x-axis. Click the "Tangent Line" box to see how the line tangent to the graph at (c,f(c)) changes as c changes. Click the "Derivative Function" box to see a graph of the derivative function. You may also pause the animation and drag the point (c,0) along the x-axis to see the relationships between the function and its derivative.
Notice that the value of the derivative function f' is the slope of the tangent line. Also, notice the significance of the places where the graph of the derivative crosses the x-axis (i.e., the zeros of the derivative).