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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. k. c. Intermediate Value Theorem. f(a). f(b). b. a. Intermediate Value Theorem.
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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.
k c Intermediate Value Theorem f(a) f(b) b a
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.
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.
Why does the I. V. T. imply that an odd degree polynomial has at least one real root?
