Use the Definition of Partial Derivatives as Limits to Find $f _ { x } ( x , y )$

question 57

Multiple Choice

Use the definition of partial derivatives as limits to find $f _ { x } ( x , y )$ if $f ( x , y ) = 5 x ^ { 2 } - 9 x y + 2 y ^ { 2 }$ .

• A) \(5 y - 9 x\)
• B) \(10 x - 9 y\)
• C) \(10 x - 9\)
• D) \(10 x - 9 x y\)
• E) \(5 x - 9 y\)

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Definitions:

Marginal Cost

The increase in expenditure resulting from the production of an additional unit of a good or service.

Short-run Cost Function

The relationship between the cost of production and the level of output when at least one input is fixed in the short term.

Long-run Cost Function

A relationship that shows the lowest possible cost at which a firm can produce any given level of output when all inputs, including capital, are variable.

Cost-output Elasticity

A measure of how responsive the cost of production is to a change in the output level.