Find the Four Second Partial Derivatives $z = x ^ { 2 } + 8 x y + 6 y ^ { 2 }$

question 82

Multiple Choice

Find the four second partial derivatives. Observe that the second mixed partials are equal. $z = x ^ { 2 } + 8 x y + 6 y ^ { 2 }$

• A) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0\)
• B) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• C) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 12 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• D) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• E) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0\)

---

Definitions:

Good Faith

An intention to act with honesty, fairness, and integrity in dealings, without seeking to deceive or defraud.

Manifest Agreement

Manifest Agreement refers to a clearly expressed or demonstrated mutual understanding or contract between parties, often requiring no further evidence to prove its existence.

Written Word

Information or content that is expressed in written form, as opposed to spoken word or other modes of communication.

Advertised Reward

An offer of payment published to the general public for the performance of a specific task, such as information leading to the recovery of lost property.