Use the Function Below and Its Derivative to Determine Any $f$

question 67

Multiple Choice

Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.
$$f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 2 } , f ^ { \prime } ( x ) = - 12 x ^ { 3 } + 12 x$$

• A) \(( - 1,3 ) , ( 0,0 ) , ( 1,3 )\)
• B) \(( - 1 , - 3 ) , ( 1 , - 12 )\)
• C) \(( - 1,3 ) , ( 1,3 )\)
• D) \(( 0,0 ) , ( 1,0 )\)
• E) \(( 0,0 ) , ( 1,3 )\)

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Definitions:

Hormone

A signaling molecule produced by glands in multicellular organisms to regulate physiology and behavior.

Behaviour

Refers to the actions or reactions of an object or organism, usually in relation to the environment.

Electro-chemical

Relating to processes that involve both electrical and chemical changes, often referring to the transmission of signals in neurons.

Neuronal Communication

The process through which neurons transmit signals to each other and to other types of cells, enabling the body to respond to stimuli.