Second Derivative Animation
Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions.
Notice how the slope of each function is the y-value of the derivative plotted below it.
For example, move to where the sin(x) function slope flattens out (slope=0), then see that the derivative graph is at zero. A similar thing happens between f'(x) and f''(x). Try this at different points and other functions.