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

question 87

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:

Metamorphosed Fossils

Fossils that have undergone metamorphism, altering their original form and composition due to heat and pressure.

Axial Surface

An imaginary surface connecting all the hinge lines of a fold or a series of folds, often perpendicular to the direction of the fold.

Moderately Inclined

Describes a structure, surface, or geological feature that is tilted or sloped at a gentle to moderate angle.

North-South

A direction or orientation aligning with the Earth's magnetic or true north and south poles.