Problem:
Using the definition of derivative, find the derivative of

f(x) = x2/3

at x = 0.


Visualization:

We calculate

The limit does not exist and, hence, f is not differentiable at x = 0.

To see graphically why that limit does not exist, we use the following MathView notebook to investigate the slopes of secant lines.

For what graphical reason, does the derivative not exist at x = 0? Answer