F(x, y) Min Max problem with boundaries

  • Thread starter Thread starter Wi_N
  • Start date Start date
  • Tags Tags
    Max
Click For Summary
The discussion revolves around finding the maximum and minimum values of the function f(x,y) constrained by the circle x^2 + y^2 = 4. Initial attempts using partial derivatives led to confusion about critical points outside the defined boundaries. After substituting y^2 with 4 - x^2 in the function, participants identified that the maximum value is 17/20 at the point (1/2, √15/4). There was clarification on the correct interpretation of the function and its constraints, emphasizing the importance of working within the defined circle. Ultimately, the conversation highlights the need for careful substitution and understanding of constraints in optimization problems.
  • #31
Correct. The numerator is not just 5, but the function is now much simpler, due to the constraint that its graph must lie on ##x^2 + y^2 = 4##.
 
  • Like
Likes Wi_N

Similar threads

Solving a min max problem in 2 variables using Mathematica
  • · Replies 6 ·
Replies
6
Views
2K
Is the Max Function a Norm in R^3?
  • · Replies 6 ·
Replies
6
Views
2K
Quadratic equation to find max and min
  • · Replies 36 ·
2
Replies
36
Views
6K
Absolute Max/Min of f(x,y)=x^2+y^2-2x on D
  • · Replies 9 ·
Replies
9
Views
3K
Finding Global Max and Min values of an Absolute Function
  • · Replies 5 ·
Replies
5
Views
1K
Another max value on surface (no boundaries)
  • · Replies 8 ·
Replies
8
Views
2K
Maximization of a Multivariable Function
  • · Replies 12 ·
Replies
12
Views
2K
How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4]
  • · Replies 2 ·
Replies
2
Views
2K
Find g(x)/h(y) for a given F(x,y)
  • · Replies 3 ·
Replies
3
Views
1K
Find f(x,y) given partial derivative and initial condition
  • · Replies 6 ·
Replies
6
Views
2K