1. Intermediate Value Theorem If f is continuous on [ a,b ] and k is any number between f(a) and f(b), inclusive, then there is at least one number c in the interval [a,b] such that f(c) = k.

2. Intermediate Value Theorem a f(a) b f(b) k c

3. Intermediate Value Theorem an existence theorem; it guarantees a number exists but doesn’t give a method for finding the number. it says that a continuous function never takes on 2 values without taking on all the values between.

4. Example Ryan was 20 inches long when born and 30 inches long when 9 months old. Since growth is continuous, there was a time between birth and 9 months when he was 25 inches long.

5. Why does the I. V. T. imply that an odd degree polynomial has at least one real root?

6. x y Do Not Assume the converse of the I.V.T.