Derivative functions > Calculating extreme values
1234Calculating extreme values

Theory

Take a look at the applet: ??

If you have a function with function rule f ( x ) then you can determine the extrema of this function as follows:

  • find the derivative of the function using differentiation and solve f ' ( x ) = 0 , taking into account the domain of the function;

  • look at the graph of the derivative function, or set up a sign plot for the derivative;

  • if f ' ( x ) moves from negative to positive for x = a (where a is within the domain of the function) then f has a (local) minimum of f ( a ) ;

  • if f ' ( x ) moves from positive to negative at x = b (where b is within the domain of the function) then f has a (local) maximum of f ( b ) .

If the sign of the derivative does not change, then there are no extrema!

Here you see an example of a sign plot for the derivative.

 

previous | next