[Solution] Find the extreme values of f(x, y)=-x^2-3 y^2+2 x+12 y on the closed triangular region with vertices of (-2,-2),(3,3), and (-2,3). Use our methods
Question: Find the extreme values of \(f(x, y)=-x^{2}-3 y^{2}+2 x+12 y\) on the closed triangular region with vertices of \((-2,-2),(3,3)\), and \((-2,3)\). Use our methods of searching/testing the boundary regions as well as the interior.
Deliverable: Word Document 
![[All Steps] Use calculus to find extreme](/images/solutions/MC-solution-library-65628.jpg "[All Steps] Use calculus to find extreme values of the function")
[All Steps] Use calculus to find extreme values of the function
(Steps Shown) Using the method of Lagrange multipliers find the
![[See Solution] If u(x, y)= cos (2](/images/solutions/MC-solution-library-65630.jpg "[See Solution] If u(x, y)= cos (2 x^2-3 y), y(r, s)=r s+3 r^2,")
[See Solution] If u(x, y)= cos (2 x^2-3 y), y(r, s)=r s+3 r^2,
![[Step-by-Step] If f(x, y)=y e^-2 x y](/images/solutions/MC-solution-library-65631.jpg "[Step-by-Step] If f(x, y)=y e^-2 x y compute the partial derivative")
[Step-by-Step] If f(x, y)=y e^-2 x y compute the partial derivative
![[Solution Library] Compute ∂ y / \partial](/images/solutions/MC-solution-library-65632.jpg "[Solution Library] Compute ∂ y / \partial z at point (s) where")
[Solution Library] Compute ∂ y / \partial z at point (s) where
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