Why Do the Steps to Maximize and Minimize a Quantity Align?

[m0286]

The question is,
The steps you follow to maximize a quantity are the same as the steps to minimize a quantity, explain why?
Im not sure why?
I know to maximize or minimize a quantity, you find the derivative, let it equal 0 and solve to find the value of the variable that results in a maximum or minimum, then you find the maximum or minimum value (if required) by substitution, then check to see you have the maximum or minimum by test-second derivative if >0 then min, if <0 max. Can anyone please explain to me why? THANKS SOO MUCH!

 

[dextercioby]

Both type of points are among the critical points.The fact that the tangent is || to the Ox axis in both situations should make the algorithms similar.And the only difference is the sign of the second derivative.

Daniel.

 

[shmoe]

Compare minimizing f(x) with maximizing -f(x).