Finding Critical Points: Solving f_x & f_y

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Homework Help Overview

The discussion revolves around finding critical points for a function defined by its partial derivatives, specifically f_x and f_y. Participants are exploring the implications of setting these derivatives to zero and the subsequent steps involved in solving the resulting equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to solve the equations f_x = 0 and f_y = 0 but expresses confusion about how to proceed after finding y = 0 and x = (6-y)/3. Other participants provide clarifications on the interpretation of the equations and suggest plugging values into the second equation.

Discussion Status

Participants are actively engaging with the problem, with some providing clarifications and others expressing their reactions to the complexity of the math involved. There is a mix of interpretations regarding the nature of the equations and the approach to solving them.

Contextual Notes

There is mention of the need for clarity in notation and the potential for quadratic equations arising from the problem setup. Participants are navigating the implications of different cases derived from the partial derivatives.

frasifrasi
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I have to find the critical points for the partials:

f_x = y/3(24 - 12x - 4y) = 0
f_y = x/3(24 - 6x - 8y) = 0

I get y = 0 and x = (6-y)/3 for x in the first partial. How am I supposed to proceed? If I plug these into the secon, it gets nasty. Can anyone demonstrate how this is done?

Thank you.
 
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First, you mean, e.g. f_x=(y/3)(24-12x-4y). Put enough parentheses into make it unambiguous. Second, you don't get y=0 AND x=(6-y)/3, you get y=0 OR x=(6-y)/3. Plug each possibility into the second equation. Third, it doesn't get 'nasty'. You get quadratic equations for x or y. That's not considered 'nasty'.
 
That is some gruesome math man.
 
Quadratics?? Are you serious?
 
Dick said:
Quadratics?? Are you serious?
LOL, you just made my night :)
 
Well, thanks. I am trying for the comedian of the year award. Aren't you the artist formerly known as rocophysics? Why the name change?
 

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