Homework Help Overview
The discussion revolves around finding the critical points of the multivariable function f(x, y) = x³ + y⁴ - 21x - 18y² and using the Second Derivative Test to classify these points. Participants are exploring the necessary steps to derive the critical points and the implications of their findings.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants attempt to solve the partial derivatives for x and y to find critical points, questioning the number of solutions expected. There is discussion about the potential for multiple solutions and the implications of missing solutions.
Discussion Status
Some participants have provided partial solutions and noted errors in previous attempts, suggesting that there are additional solutions to consider. The conversation reflects a collaborative effort to clarify misunderstandings and explore different approaches to the problem.
Contextual Notes
Participants express uncertainty regarding the number of critical points and the validity of their solutions, particularly in relation to the requirement for six different critical point answers. There is also mention of the need to consider solutions that may have been overlooked.