text: cal3
  
  posted by on .
  
  Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy
  
  • cal3 - ,
  
  F = -3yx^2-3xy^2+36xy
  Fx = -6xy - 3y^2 + 36y
  Fxx = -6y
  
  Fy = -3x^2 - 6xy + 36x
  Fyy = -6x
  
  Fxy = -6x - 6y + 36
  
  D = FxxFyy-(Fxy)^2 = 36xy - 36(x+y-6)^2
  
  Fx = 0 Fy=0 at (0,0)
  
  Fx = -6xy - 3y^2 + 36y
  Fx = 0 when y = 2(6-x)
  
  Fy = -3x^2 - 6xy + 36x
  Fy = 0 when x = 2(6-y)
  
  So there is a local max for z along those two lines
  
  • cal3 - ,
  
  Okay Im just confused as how to get Fx=0 and Fy=0, If I set -6xy-3y^2+36y=0 how do i solve this?? Algebra was so long ago!
  could you detail that part of the problem...
explanation: The text extract is a discussion or solution to a calculus problem, specifically finding and classifying the critical points of a function of two variables. The extract contains a question and a detailed answer, including the steps to find the partial derivatives and the conditions for critical points.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: cal3
  
  posted by on .
  
  Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy
  
  • cal3 - ,
  
  F = -3yx^2-3xy^2+36xy
  Fx = -6xy - 3y^2 + 36y
  Fxx = -6y
  
  Fy = -3x^2 - 6xy + 36x
  Fyy = -6x
  
  Fxy = -6x - 6y + 36
  
  D = FxxFyy-(Fxy)^2 = 36xy - 36(x+y-6)^2
  
  Fx = 0 Fy=0 at (0,0)
  
  Fx = -6xy - 3y^2 + 36y
  Fx = 0 when y = 2(6-x)
  
  Fy = -3x^2 - 6xy + 36x
  Fy = 0 when x = 2(6-y)
  
  So there is a local max for z along those two lines
  
  • cal3 - ,
  
  Okay Im just confused as how to get Fx=0 and Fy=0, If I set -6xy-3y^2+36y=0 how do i solve this?? Algebra was so long ago!
  could you detail that part of the problem...
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is a discussion or solution to a calculus problem, specifically finding and classifying the critical points of a function of two variables. The extract contains a question and a detailed answer, including the steps to find the partial derivatives and the conditions for critical points.
  
  Label: question-and-answer