Question

What does it mean for a function to have an absolute extreme value at a point c of an interval [a,b]

Answer 1

Hello from MrBillDoesMath!

Answer: Suppose the function is f(x). The statement means that either:

1) f(c) >= f(x) for x in the interval [a,b]

or

2) f(c) <= f(x) for x in the interval [a,b]

That is, the value of f(c) is larger (or smaller, take your choice) than the value of f(x) for all other x in the interval. Equivalently, f(c) is the largest (or smallest) value of f(x) in the interval.

Regards, MrB