Find the Maximum Rate of Change Of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$

question 30

Multiple Choice

Find the maximum rate of change of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$ at the point $( 2,1 )$ . In what direction does it occur?

• A) \(\frac { 85 } { 2 } , \left( 2 , \frac { 7 } { 2 } \right)\)
• B) \(\frac { 29 } { 2 } , \left( 1 , \frac { 9 } { 2 } \right)\)
• C) \(\frac { \sqrt { 29 } } { 2 } , \left( 1 , \frac { 5 } { 2 } \right)\)
• D) \(\frac { \sqrt { 85 } } { 2 } , \left( 1 , \frac { 9 } { 2 } \right)\)
• E) none of these

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Definitions:

Human Capital

The economic value of the skills, knowledge, and experiences possessed by an individual or population.

Real GDP

The measure of a country's economic output adjusted for price changes, such as inflation or deflation, providing a more accurate reflection of an economy's size and health.

Percent

A mathematical term representing a part per hundred in everything from finance to statistics.

Economic Growth

An increase in the amount of goods and services produced per head of the population over a period of time, often measured as the percent rate of increase in real gross domestic product (GDP).