A Point Moves Along the Curve $3 y + y ^ { 2 } - 8 x = 2$

question 15

Multiple Choice

A point moves along the curve $3 y + y ^ { 2 } - 8 x = 2$ . When the point is at $\left( - \frac { 1 } { 2 } , - 1 \right)$ , its $x$ -coordinate is increasing at the rate of 3 units per second. How fast is its $y$ -coordinate changing at that instant of time?

• A) 24 units/sec
• B) 26 units \(/ \mathrm { sec }\)
• C) \(- 24\) units/sec
• D) \(- 22\) units/sec

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Definitions:

Facial Expressions

The movements of the muscles beneath the skin of the face, used as non-verbal communication to convey emotions and reactions.

Posture

The way in which someone holds their body when standing or sitting, often reflecting confidence, attitude, or current state of health.

Vocal Intonations

The variation in pitch while speaking, which can affect the meaning, emotion, or emphasis conveyed by the speaker.

Intrusive Rock

An igneous rock that solidified from magma below Earth’s surface; synonym: plutonic rock.