A local minimum is a point on a curve or surface where the value of the function is less than all nearby points, but not necessarily the lowest point on the entire curve or surface. In other words, it is a valley or dip on the function that is surrounded by higher values on all sides.
This can be described formally by saying there exists a local minimum of the function
Local minimums can be found by analytically by using either the first derivative test or the second derivative test. Alternatively local minimums can be found graphically by looking where the graph reaches a valley or dip.