Finding Max & Min of Optimization Problem: How To Distinguish

  • Context: MHB 
  • Thread starter Thread starter thinkbot
  • Start date Start date
  • Tags Tags
    Optimization
Click For Summary

Discussion Overview

The discussion centers on the differences between finding the maximum and minimum values in optimization problems, specifically how to distinguish between them within equations. It involves theoretical aspects of calculus, particularly the use of derivatives to identify critical points and determine the nature of these points.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants note that finding critical values is a common step for both maximum and minimum problems, suggesting the use of first or second derivative tests to determine the nature of these extrema.
  • One participant expresses familiarity with the derivative tests and seeks a brief explanation of how they function.
  • Another participant reiterates the process of finding critical numbers and mentions using the second derivative test to identify whether the critical points correspond to maxima or minima.
  • There is a request for clarification on the rationale behind the first and second derivative tests for relative extrema, indicating a desire for deeper understanding.

Areas of Agreement / Disagreement

Participants generally agree on the process of finding critical values and the application of derivative tests, but there is no consensus on the detailed rationale behind these tests, as some seek further explanation.

Contextual Notes

Some assumptions about the familiarity with calculus concepts may be present, and the discussion does not resolve the underlying rationale for the derivative tests.

thinkbot
Messages
5
Reaction score
0
How are Finding the max and min of a optimization problem different. and how do you distinguish them in an equation?
 
Physics news on Phys.org
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?
 
Yes I am familiar
 
thinkbot said:
Yes I am familiar

Can you briefly explain how they work? :D
 
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.
 
thinkbot said:
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.
 

Similar threads

Graduate How to Find Critical Points of function f(x,y,z)
  • · Replies 9 ·
Replies
9
Views
3K
MHB Is Completing the Square Necessary for Finding Optimal Points in Calculus?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Optimization of multiple integrals
  • · Replies 2 ·
Replies
2
Views
2K
MHB Optimization - Lagrange multipliers : minimum cost/maximum production
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find a,b,c,d given max and min in cubic function
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Calculate acceleration from power/torque graphs
  • · Replies 17 ·
Replies
17
Views
1K
MHB What Are the Absolute Max/Min of f(x) Over Given Intervals?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solve Optimization Problem: Find Min & Max of f(x,y)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Optimization problem: Error mitigation while using trigonometry
  • · Replies 18 ·
Replies
18
Views
3K
MHB How Do You Find the Absolute Min and Max of a Function on a Triangular Region?
  • · Replies 4 ·
Replies
4
Views
3K