1 more quick calculus question

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In summary, the conversation discusses the similarities between the steps for maximizing and minimizing a quantity, specifically finding the derivative, solving for the variable, and using a test-second derivative. The only difference between the two is the sign of the second derivative. It is mentioned that both types of points are critical points and the fact that the tangent is parallel to the x-axis in both situations makes the algorithms similar. Finally, the conversation also briefly touches on the comparison between minimizing f(x) and maximizing -f(x).
  • #1
m0286
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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!
 
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  • #2
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.
 
  • #3
Compare minimizing f(x) with maximizing -f(x).
 

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