A local maximum is a point on a curve or surface where the value of the function is greater than all nearby points, but not necessarily the highest point on the entire curve or surface. In other words, it is a peak or hill on the function that is surrounded by lower values on all sides.
This can be described formally by saying there exists a local maximum of the function
Local maximums can be found by analytically by using either the first derivative test or the second derivative test. Alternatively local maximums can be found graphically by looking where the graph reaches a peak or hill.