Find the Equation of the Function Whose Derivative Is $f ^ { \prime } ( x ) = \frac { x ^ { 2 } + 9 x + 7 } { x - 1 }$

question 9

Multiple Choice

Find the equation of the function whose derivative is $f ^ { \prime } ( x ) = \frac { x ^ { 2 } + 9 x + 7 } { x - 1 }$ and whose graph passes through the point $( 2,4 )$ .

• A) \(\frac { x ^ { 2 } } { 2 } + 10 x + 17 \ln | x - 1 | - 19\)
• B) \(\frac { x ^ { 2 } } { 2 } + 9 x + 17 \ln | x - 1 | - 18\)
• C) \(\frac { x ^ { 2 } } { 2 } + 10 x + 17 \ln | x - 1 | - 18\)
• D) \(\frac { x ^ { 2 } } { 2 } + 9 x + 7 \ln | x - 1 | - 18\)
• E) \(\frac { x ^ { 2 } } { 2 } + 10 x + 7 \ln | x - 1 | - 19\)

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Definitions:

Terminal Branches

The ends of axons in the nervous system, responsible for releasing neurotransmitters to send signals to other neurons or muscles.

Autonomic Nervous System

The autonomic nervous system is a control system that acts largely unconsciously and regulates bodily functions, such as the heart rate, digestion, respiratory rate, pupillary response, and more.

Somatic Nervous System

A part of the peripheral nervous system that controls voluntary movements of the body and transmits sensory information to the central nervous system.

Spinal Reflex System

A part of the nervous system responsible for reflex actions, which are automatic and involuntary responses to stimuli, processed through the spinal cord.