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Intermediate Value Theorem

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

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

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

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