The discussion focuses on finding the maximums, minimums, and saddle points of the function Z = 4Y³ + X² - 12Y² - 36Y + 2. Participants emphasize the importance of calculating the partial derivatives with respect to X and Y, setting them equal to zero to find critical points. Despite initial confusion regarding the lack of substitutions, it is established that solutions exist, and participants are encouraged to show their work for clarity.
PREREQUISITESStudents in calculus courses, educators teaching optimization methods, and anyone interested in multivariable function analysis.
Baumer8993 said:Homework Statement
Find the maximums, minimums, and saddle points (if any) of
Z = 4Y3 + X2 - 12Y2 - 36Y +2
Homework Equations
The partial derivatives with respect to X , and Y.
The Attempt at a Solution
I took the two partials, and set them equal to zero. The problem is that there is not anything to substitute, and when I tried solving them there was no solution.