Find the Slope of the Curve at the Given Point $$y = x ^ { 3 } - 8 x , P ( 1 , - 7 )$$

question 29

Multiple Choice

Find the slope of the curve at the given point P and an equation of the tangent line at P.
- $$y = x ^ { 3 } - 8 x , P ( 1 , - 7 )$$

• A) slope is \(- 5 ; y = - 5 x - 2\)
• B) slope is \(3 ; y = 3 x - 6\)
• C) slope is \(- 5 ; y = - 5 x\)
• D) slope is \(3 ; y = 3 x - 10\)

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Definitions:

Decreasing-cost Industry

An industry in which costs per unit decrease as the scale of operation increases, often due to economies of scale.

Downsloping

A characteristic of certain economic graphs, such as the demand curve, indicating that as price decreases, quantity demanded increases.

Purely Competitive Firm

A business that operates in a market where there are many buyers and sellers, and it has no control over the market price of its product.

Economic Profit

The difference between a firm’s total revenue and its opportunity costs (including both explicit and implicit).