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

question 4

Multiple Choice

Find the maximum rate of change of $f ( x , y ) = x y ^ { 2 } + \sqrt { y }$ at the point $( 4,1 )$ (2,1) . In what direction does it occur?

• A) \(\frac { \sqrt { 29 } } { 2 } , \left\langle1 , \frac { 5 } { 2 } \right\rangle\)
• B) \(\frac { 85 } { 2 } , \left\langle2 , \frac { 7 } { 2 } \right\rangle\)
• C) \(\frac { 29 } { 2 } , \left\langle 1 , \frac { 9 } { 2 } \right\rangle\)
• D) \(\frac { \sqrt { 293 } } { 2 } , \left\langle1 , \frac { 17 } { 2 } \right\rangle\)
• E) none of these

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Definitions:

Cluster Sample

A sampling method where the population is divided into clusters, and a random sample of these clusters is chosen for analysis.

Rows

In the context of data, rows represent individual records or observations in a database or table.

Average Age

The mean age of a group of individuals, calculated by adding their ages together and dividing by the total number of individuals.

Voluntary Response Sampling

A sampling method in which participants self-select to be part of a survey or study, often leading to biased results due to non-random participation.