[list][*]Use the input box to define the function f(x). [/*][*]Use the checkboxes for f(x), f'(x), and f''(x) to show/hide the graphs of the function, its first derivative, and its second derivative, respectively. [/*][*]Use the Tangent checkboxes to show/hide tangent lines on the graph of f and the graph of f', respectively. [/*][/list]

Given a function y = f(x), the derivative f'(x) is a function whose values represent the rate of change of f. Because y = f'(x) is itself a function, it has its own rate of change, i.e., derivative. The derivative of the derivative of f is called the [b]second derivative[/b] of f:[br][br][math]f''(x)=\frac{d}{dx}\left[f'(x)\right]=\frac{d}{dx}\left[\frac{d}{dx}\left[f(x)\right]\right][/math][br][br]Because the derivative operator [math]\frac{d}{dx}[/math] is applied to y = f(x) twice, the following notation is also frequently used to represent the second derivative:[br][br][math]f''(x)=\frac{d^2y}{dx^2}[/math][br][br]Whereas the first derivative tells us how fast f is changing and can be thought of like [i]speed/velocity[/i] of f, the second derivative tells us how fast f' is changing and can be thought of like [i]acceleration [/i]of f.