A Function and Its Graph Are Given $y = f ( x )$

question 56

Multiple Choice

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of $y = f ( x )$ . Check these results against the graph shown. $$y = 18 x ^ { 4 } - 54 x ^ { 2 } + 36$$

• A) \(x = - \frac { \sqrt { 2 } } { 2 }\)
• B) \(x = 0\)
• C) \(x = \frac { \sqrt { 2 } } { 2 }\)
• D) \(x = \frac { \sqrt { 2 } } { 2 }\) , \(x = - \frac { \sqrt { 2 } } { 2 }\)
• E) \(x = - \frac { \sqrt { 2 } } { 2 }\) , \(x = 0\) , \(x = - \frac { \sqrt { 2 } } { 2 }\)

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Definitions:

Motor Nerves

Nerves that carry impulses away from the central nervous system to muscles, stimulating them to contract and produce movement.

Sensory Nerves

Nerves that transmit sensory information from the body to the central nervous system, informing about external and internal environments.

Opiate Drugs

Substances derived from the opium poppy that are used for their pain-relieving properties but may lead to addiction.

Receptor Sites

Specific locations on the surface of a cell or within its interior where chemical compounds, such as hormones or neurotransmitters, can bind to trigger a response in the cell.