relative/local maximum
-at c if f(c) is greater than or equal to f(x) for all x in a neighborhood of c
A relative/local maximum is a point on a graph where the function attains its highest value in a certain interval, but may not be the highest point on the entire graph.
More formally, a point (a,b) is a relative/local maximum of a function f(x) if there exists an interval (c,d) such that b ≥ f(x) for all x in (c,d) and b = f(a).
To find a relative/local maximum, we can take the derivative of the function and set it equal to zero to find the critical points. Then, we can check the values of the function at those critical points as well as the values before and after them in order to determine whether they represent relative/local maxima.
Note that a relative/local maximum may also be a global/absolute maximum if it is the highest point on the entire graph.
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