Find All Relative Extrema of the Function $f ( x ) = 4 x ^ { 4 } - 16 x ^ { 3 } + 5$

question 1

Multiple Choice

Find all relative extrema of the function $f ( x ) = 4 x ^ { 4 } - 16 x ^ { 3 } + 5$ Use the Second Derivative Test where applicable.

• A)relative max: \(f ( 6 ) = 1733\) ; no relative min
• B)relative max: \(f ( 3 ) = 103\) ; no relative min
• C)no relative max or min
• D)relative min: \(f ( 6 ) = 1733\) ; no relative max
• E)relative min: \(f ( 3 ) = - 103\) ; no relative max

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Definitions:

Irrational Beliefs

Thoughts or beliefs that are unrealistic, illogical, and unhelpful, often contributing to negative emotional states and behaviors in cognitive-behavioral therapy contexts.

LFT

Liver Function Tests, a group of blood tests that evaluate the health and performance of the liver by measuring levels of enzymes, proteins, and substances in the blood.

Disputing Irrational

A cognitive-behavioral therapy technique aimed at challenging and modifying irrational beliefs and thoughts.

Substance Use

The consumption of drugs or alcohol, which can range from moderate use to dependency and addiction.