intermediate value theorem if f is continuous on [ a,b ] and k is any number between f(a) and f(b),...
TRANSCRIPT
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.
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.
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.