Find Global Extrema of Functions: Steps & Example

[Ali Asadullah]

Please check my steps for global extrema of functions.
1) Finding Critical points.
2) Finding values of f at critical points and end-points.
3) Checking which one is largest and which is smallest.
4) Largest would be Global maxima and the smallest would be minima.

Now a question, i know how to find global extrema if they are at
end-points. How can i find local extrema if they occur at end-points?
I will be thankful to you if you illustrate it with a simple example.

 

[HallsofIvy]

Strictly speaking, and endpoint is always a "local extremum". If the function is increasing there, then the endpoint is either a max or a min depending on which side the interval is. If the function is decreasing, then that is reversed.