Intermediate Value Theorem
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Transcript of 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.
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Intermediate Value Theorem
a
f(a)
bf(b)
k
c
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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.
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ExampleRyan 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.
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Why does the I. V. T. imply that an odd degree polynomial has at least one real root?
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x
y
Do Not Assume the converse of the I.V.T.