At the Given Point, Find the Slope of the Curve $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 12 x$

question 362

Multiple Choice

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve,
as requested.
- $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 12 x$ , slope at $( 0,1 )$

• A) \(- \frac { 7 } { 2 }\)
• B) \(\frac { 12 } { 5 }\)
• C) \(\frac { 12 } { 7 }\)
• D) 4

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Definitions:

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Conditions that impact the brain's structure and function, impairing mental processes and behaviors.

Sensory Receptors

Cells or structures specialized to detect changes in the environment and convey the information to the nervous system.

Ruffini End Organ

Receptor located deep in the dermis and responding to continuous touch or pressure. Named for Italian histologist Angelo Ruffini (1864–1929).

Pacinian Corpuscle

A type of mechanoreceptor found in the skin and various internal organs that detects pressure and vibration.