Extreme value theorem
In
calculus, the
extreme value theorem states that if a function
f(
x) is
continuous in the closed interval [a,b] then
f(
x) must attain its maximum and minimum value, each at least once.
That is, there exist numbers c, and d withinin the interval [a, b] such that for every value of x in [a, b],
The extreme value theorem is used to prove
Rolle's theorem.
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