The discussion revolves around finding the critical points of a function of two variables, specifically f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2 + 100. Participants express uncertainty regarding the implications of the x^3 term in the function and how it affects the process of finding critical points.
Some participants have offered guidance on setting the components of the partial derivatives to zero, while others are questioning the interpretation of the derivatives and the nature of critical points. Multiple interpretations of the problem are being explored, and there is an ongoing exchange of ideas without a clear consensus.
Participants are grappling with the definitions and implications of critical points, particularly in relation to the behavior of the function's derivatives. There is a mention of confusion regarding whether critical points are defined solely by the first derivatives being zero or if other conditions apply.
Chadlee88 said:Partial derivatives
(6x^2+y^2+10x)i + (2xy+2y)j
how am i supposed to find values of x and y that make it equal to zero??
the partial derivative with respect to x is a quadratic function with both x and y terms. so I'm stuck!
Dick said:You shouldn't really have components anyway. The partial derivatives aren't a vector. Start with the second one 2xy+2y=0.