Choose two values for the independent variable close to the turning-point. By comparing the f(x) values on either side of the extremum you can see if these are bigger or smaller. For example, at (c,f(c)) we have an extremum for f(x). Choose a small arbitrary value h and calculate f(c-h) and f(c+h). If both of these are less than f(c) then we have a maximum.
