AS/A2 Pure 1 Pure 2

P3 Topic 4: Differentiation
The gradient of ax
The graph shows an example of exponential growth. Compare the graph of y=ax with the graph of its gradient function. The gradient function is axln a. Adjust the value of a until the two curves coincide.

Summary The curve y=ax and its gradient function, axln a coincide when a = 2.718... The number 2.718... is called e, and is a very important number in calculus. Based on free Java applets from JavaMath