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What is an example of a function that is continuous on the interval a b for which the conclusion of the mean value theorem does not hold?
Adomonster
Let f(x)=abs(x) , absolute value of x defined on the interval [5,5]
f(x)= |x| , -5 ≤ x ≤ 5
Then, f(x) is continuous on [-5,5], but not differentiable at x=0 (that is not differentiable on (-5,5)). Therefore, the Mean Value Theorem does not hold.
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