Find the four second partial derivatives. Observe that the second mixed partials are equal.

z = x ^ { 2 } + 8 x y + 6 y ^ { 2 }

\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0

\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8

\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 12 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8

\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8

\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0

A Company Sells Two Products Whose Demand Functions Are Given

Multiple Choice