Finding the rate of change of the function (how does y change as x changes). The red line is the Secant line between A and B. The green line is the tangent to the curve at the point A. The slopes of each line are shown. The position of the points A and B can be moved giving different secant lines and different tangents.

What happens when the point B comes closer to the point A? Note the slope of the Secant and the slope of the Tangent.

This applet allows different exponential graphs to be displayed by adjusting the slider. The slope of the tangent at a point is also displayed and the point can be moved along the curve. The graph of e^x can also be displayed along with a tangent and slope for comparison.

By moving the slider can you find what is the value of e? Examining the graph of e^x, does the slope of the tangent show any relationship with the point where it meets the curve?