Increasing and decreasing functions:
Extreme values calculus is defined by Fermat's theorem, which states that they must occur at critical points.
If f(x) has an extremum on an open interval, then the extreme value occurs at a critical point of f(x).
If f(x) has an extremum on a closed interval, then the extreme value occurs either at a critical point or at an endpoint.
Critical points of f(x) are defined as the values of x* for which either f'(x*) = 0 or f’(x*) does not exist.
One can distinguish whether an extremum is a local maximum or local minimum by using the first derivative test or second derivative test.
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