Local minima and maxima (First Derivative Test) A function has a local maximum or relative maximum at a point if the values of for 'near' are all less than . Thus, the graph of near has a peak at . A function has alocal minimum or relative minimum at a point if the values of for 'near' are all greater than .
real-valued functionf defined on a domainX has a globalmaximum point at a if f(a) ≥ f(x) for all x in X. Similarly, the function has a globalminimum point at a if f(a) ≤ f(x) for all x in X. The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function.