The Intermediate Value Theorem
The Intermediate Value Theorem tells us that if is a continuous function on a closed interval , and if is any value between and , then for some in .
This interactive figure demonstrates the Intermediate Value Theorem for a few examples. You can move the points , , and . You can change the function, but this figure will not work with arbitrary discontinuous functions.
If the points you drag disappear after being dragged off the screen, you can reset them by selecting a new example.
Developed for use with Thomas' Calculus, published by Pearson.