Second Derivative Animation

Here we can play with the derivative f'(x) and the second derivative f''(x) of some common functions.

Notice how the slope of each graph equals the y-value of the derivative plotted directly below it.

For example, find a point where the slope flattens out (becomes zero), and notice that the derivative graph crosses zero right there too.

A similar thing happens between f'(x) and f''(x). Try this at different points and different functions.