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...
The text passage is a discussion or solution to a calculus problem, specifically finding and classifying critical points of a multivariable function. It includes a question about how to solve for the points where the partial derivatives are zero.
single_question_with_answer

the passage contains a single mathematical question (how to solve for fx=0 and fy=0) and provides a partial answer (the lines where the critical points occur). however, the answer is not fully detailed, as the asker is confused about the algebraic steps to solve the equations.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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...
user
The text passage is a discussion or solution to a calculus problem, specifically finding and classifying critical points of a multivariable function. It includes a question about how to solve for the points where the partial derivatives are zero.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question (how to solve for Fx=0 and Fy=0) and provides a partial answer (the lines where the critical points occur). However, the answer is not fully detailed, as the asker is confused about the algebraic steps to solve the equations.