Find the Slope of the Curve at the Given Point $y = x ^ { 3 } - 9 x , P ( 1 , - 8 )$

question 209

Multiple Choice

Find the slope of the curve at the given point P and an equation of the tangent line at P.
- $y = x ^ { 3 } - 9 x , P ( 1 , - 8 )$

• A) slope is \(- 6 ; y = - 6 x\)
• B) slope is \(3 ; y = 3 x - 11\)
• C) slope is \(3 ; y = 3 x - 7\)
• D) slope is \(- 6 ; y = - 6 x - 2\)

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Definitions:

Negative Punishment

A behavior modification technique where a desirable stimulus is removed following an unwanted behavior, with the aim of decreasing that behavior in the future.

Stimulus Generalization

A psychological phenomenon in which a response to a specific stimulus becomes associated with similar stimuli, leading to the same response to the similar stimuli.

Secondary Reinforcer

A stimulus that has become reinforcing through its association with a primary reinforcer, often used in behavioral training and conditioning.

Primary Reinforcer

A stimulus that satisfies a basic biological need, such as food or water, and is inherently rewarding.