The [b]Intermediate Value Theorem[/b] tells us that if [math]f[/math] is a continuous function on a closed interval [math][a,b][/math], and if [math]y_0[/math] is any value between [math]f(a)[/math] and [math]f(b)[/math], then [math]y_0=f\left(c\right)[/math] for some [math]c[/math] in [math][a,b][/math].[br][br]This interactive figure demonstrates the Intermediate Value Theorem for a few examples. You can move the points [math]a[/math], [math]b[/math], and [math]y_0[/math]. You can change the function, but this figure will not work with arbitrary discontinuous functions.[br][br]If the points you drag disappear after being dragged off the screen, you can reset them by selecting a new example.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]