Given $f ( x ) = x ^ { 2 } + 6 x$

question 154

Multiple Choice

Given $f ( x ) = x ^ { 2 } + 6 x$ .
(a) Find the intervals on which $f$ is increasing or decreasing.
(b) Find the relative maxima and relative minima of $f$ .

• A) (a) Increasing on \(( - 3 , \infty )\),
• decreasing on \(( - \infty , - 3 )\)
• (b) Rel. min. \(f ( - 3 ) = - 9\)
• B) (a) Increasing on \(( - \infty , - 3 )\),
• decreasing on \(( - 3 , \infty )\)
• (b) Rel. max. \(f ( - 3 ) = - 9\)
• C) (a) Increasing on \(( - 6 , \infty )\),
• decreasing on \(( - \infty , - 6 )\)
• (b) Rel. min. \(f ( - 6 ) = 0\)
• D) (a) Increasing on \(( - \infty , - 6 )\),
• decreasing on \(( - 6 , \infty )\)
• (b) Rel. max. \(f ( - 6 ) = 0\)

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Definitions:

Cerebellum

A part of the brain at the back of the skull in vertebrates, which coordinates and regulates muscular activity.

Clumsy

Lacking coordination in movement or in handling objects, often leading to accidents or awkwardness.

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Lacking the ability to move or react in a smooth, efficient, and purposeful manner, often due to deficiencies in motor skills or spatial awareness.

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A brain structure involved in the sense of smell, processing odors and transmitting information to other parts of the brain.