For the Function $f ( x , y ) = x ^ { 2 } y ^ { 3 }$

question 73

Multiple Choice

For the function $f ( x , y ) = x ^ { 2 } y ^ { 3 }$ find a unit vector in the direction of the steepest increase at the point (a, b) = (1, 1) .

• A) \(\vec { u } = \frac { 2 } { \sqrt { 13 } } \vec { i } - \frac { 3 } { \sqrt { 13 } } \vec { j }\)
• B) \(\vec { u } = 2 \vec { i } + 3 \vec { j }\)
• C) \(\vec { u } = \frac { 2 } { \sqrt { 13 } } \vec { i } + \frac { 3 } { \sqrt { 13 } } \vec { j }\)
• D) \(\vec { u } = \frac { 2 } { \sqrt { 13 } } \vec { i } + \frac { 6 } { \sqrt { 13 } } \vec { j }\)

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Definitions:

Appropriate

Suitable or proper in the circumstances.

Overhead Costs

Indirect costs not directly tied to production, such as rent, utilities, and administrative expenses, necessary for running a business.

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A production system where materials flow continuously through an uninterrupted production process, aiming for high efficiency and constant output.

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A document detailing the total costs associated with manufacturing a product, including materials, labor, and overhead expenses.