Find the Function with the Given Derivative Whose Graph Passes $f ^ { \prime } ( x ) = x - 6 , P ( 3 , - 8 )$

question 287

Multiple Choice

Find the function with the given derivative whose graph passes through the point P.
- $f ^ { \prime } ( x ) = x - 6 , P ( 3 , - 8 )$

• A) \(f ( x ) = x ^ { 2 } - 6 x + 1\)
• B) \(f ( x ) = \frac { x ^ { 2 } } { 2 } - 6 x + \frac { 13 } { 2 }\)
• C) \(f ( x ) = x ^ { 2 } - 6 x\)
• D) \(f ( x ) = \frac { x ^ { 2 } } { 2 } - 6 x + \frac { 11 } { 2 }\)

---

Definitions:

Spinal Cord

The Spinal Cord is a crucial part of the central nervous system housed within the spinal column, responsible for transmitting neural signals between the brain and the rest of the body.

Heartbeat and Breathing

The physiological processes of cardiac rhythm and pulmonary ventilation that are essential to oxygenate the blood and remove carbon dioxide.

Medulla

The lower part of the brainstem, controlling vital functions such as heart rate and breathing.

Little Brain

A colloquial term for the cerebellum, a region of the brain that plays important roles in motor control and cognitive functions.