Second Derivative Animation

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

Notice the slope of each function is the y-value of the derivative plotted below it.

For example, find a point where the slope of the sin(x) function becomes zero (i.e., where the curve flattens), and notice that the derivative graph intersects the x-axis at these points, in other words x=0.

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