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

Recognize the differences and relationships between population and sample.

Understanding the concept and calculation of simple statistical inferences.

Differentiating between various types of data (univariate, bivariate, multivariate).

Applying statistical methods to real-world problems.

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Definitions:

Unit Product Cost

The total cost incurred to produce, package, and place a product ready for sale, divided by the number of units produced.

Absorption Costing

An accounting method that includes all manufacturing costs—direct materials, direct labor, and both variable and fixed overhead—in the cost of a product.

Unit Product Cost

The calculation of the total cost (including materials, labor, and overhead) to produce a single unit of a product.

Variable Costing

A costing method in which all variable manufacturing costs are included as inventoriable costs, while fixed manufacturing overhead is treated as an expense of the period.