Provide an Appropriate Response $\mathrm { P } _ { 0 }$

question 384

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $\mathrm { P } _ { 0 }$ .
$$f ( x , y ) = x e ^ { y } - \ln ( x ) , P _ { 0 } ( - 3,0 )$$

• A) \(\left( - \frac { 9 } { \sqrt { 97 } } \right) i + \left( \frac { 4 } { \sqrt { 97 } } \right) j\)
• B) \(\left( - \frac { 4 } { \sqrt { 97 } } \right) \mathrm { i } - \left( \frac { 9 } { \sqrt { 97 } } \right) \mathrm { j }\)
• C) \(\left( - \frac { 4 } { \sqrt { 97 } } \right) \mathrm { i }\)
• D) \(\left( \frac { 4 } { \sqrt { 97 } } \right) \mathrm { i } - \left( \frac { 9 } { \sqrt { 97 } } \right) \mathrm { j }\)

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Definitions:

Nail Matrix

The tissue under the nail that is responsible for producing cells that become the nail plate.

Lunula

The visible part of the root of a nail, often appearing as a whitish half-moon shape at the base of the fingernail or toenail.

Nail Groove

The depression or groove in the skin in which the sides of the nail are embedded, playing a critical role in nail growth and health.

Apocrine Sweat Glands

Apocrine sweat glands are a type of gland found in various parts of the body associated with hair follicles; they secrete a milky sweat that produces body odor when decomposed by bacteria on the skin.