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
