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:

Initial Direct Costs

The expenditures that a company can directly attribute to acquiring a new lease or originating a loan.

Operating Lease

A lease agreement that allows for the use of an asset but does not convey rights similar to ownership of the asset.

Prepaid Asset

Costs that are paid for upfront and listed as assets prior to their utilization or consumption.

Interest Rate Implicit

The interest rate in a lease that, when applied to the lease payments, discounts them to equal the fair value of the leased asset.