In the initial example, one fixed point is [b]repelling[/b] and one is [b]attracting[/b]. [br][br]Whether a fixed point is attracting or not, depends on the derivative of the function at the fixed point. [br][br]Change [math]f\left(x\right)[/math][math][/math]to a linear function (using the coefficients [math]m[/math] and [math]c[/math]) . Change the value of [math]m[/math] to see what values yield an attracting fixed point. [br][br]Make a conjecture! What condition must be true in order for a fixed point to be an attracting fixed point? [br][br](In order to prove the conjecture, you can use Taylor expansion to make a linear approximation of the function.)