Find an Equation for the Tangent to the Curve at the Given

question 487

Multiple Choice

Find an equation for the tangent to the curve at the given point.
- $$f ( x ) = 10 \sqrt { x } - x + 3 , ( 100,3 )$$

• A) \(y = 3\)
• B) \(y = - \frac { 1 } { 2 } x + 3\)
• C) \(y = \frac { 1 } { 2 } x - 53\)
• D) \(y = - \frac { 1 } { 2 } x + 53\)

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Definitions:

Pure Competition

A market structure characterized by a large number of small firms producing identical products with no barriers to entry or exit.

Economic Profits

The difference between the total revenue from sales and the total costs of production, including both explicit and implicit costs, representing excess earnings above the normal profit level.

Demand Curve

An illustrated curve that demonstrates how demand for a product decreases as its price increases, commonly presented with a downward trajectory.

Average Total Cost

The cost per unit of output, calculated by dividing the total cost (both fixed and variable) by the total quantity produced.