MHB Finding Max & Min of Optimization Problem: How To Distinguish

[thinkbot]

How are Finding the max and min of a optimization problem different. and how do you distinguish them in an equation?

 

[MarkFL]

Finding the critical values is the same, and then we can use either the first or second derivative tests to determine the nature of the extremum, or whether it is actually an extremum or not.

Are you familiar with these two tests?

 

[thinkbot]

Yes I am familiar

 

[MarkFL]

Yes I am familiar

Can you briefly explain how they work? :D

 

[thinkbot]

find f^1(x) = 0 x('s)= critical numbers plus some points (a,b) or [a,b]
f(x,a,b) = extrema Larget # max smallest # min
Using f^2(x) for the critical #'s f2(x) > 0 then min and ect.

 

[MarkFL]

find f^1(x) = 0 x('s)= critical numbers plus some points (a,b) or [a,b]
f(x,a,b) = extrema Larget # max smallest # min
Using f^2(x) for the critical #'s f2(x) > 0 then min and ect.

I meant can you explain how and why the first and second derivative tests for relative extrema work, i.e., the rationale behind them.