When solving f(x) = 0 \, in situations where the derivative f'(x) of a function is difficult to find, the Newton-Raphson method will be inappropriate. This problem can be overcome by approximating the derivative. In this case we will need two approximations x_0 and x_1 to the root of the equation f(x)=0 \,. The line through (x_0, f(x_0)) and (x_1, f(x_1)) is called a secant and where it crosses the x-axis is taken as our next approximation, x_2, to the root.
This root can be found using: x_{2} = \displaystyle \frac{x_0f(x_1)- x_1f(x_0)}{f(x_1)-f(x_0)}
This applet demonstrates finding a the root of a function f(x) by the Secant Algorithm. How well this method works depends on how well we choose the initial two points.
To run the demo:

1. Choose a function.
2. Click the mouse on the graph along the x axis to pick the two starting points. For the best results, the second point should be closer to the root.
3. Press the Step button to single-step the algorithm.
4. Press the Run button to animate the algorithm.