$\text { Determine the open intervals on which the graph of } y = - 6 x ^ { 3 } + 8 x ^ { 2 } + 6 x - 5 \text { is }$

question 32

Multiple Choice

$\text { Determine the open intervals on which the graph of } y = - 6 x ^ { 3 } + 8 x ^ { 2 } + 6 x - 5 \text { is }$ concave downward or concave upward.

• A) concave downward on \(( - \infty , \infty )\)
• B) concave upward on \(\left( - \infty , - \frac { 4 } { 9 } \right) ;\) concave downward on \(\left( - \frac { 4 } { 9 } , \infty \right)\)
• C) concave upward on \(\left( - \infty , \frac { 4 } { 9 } \right) ;\) concave downward on \(\left( \frac { 4 } { 9 } , \infty \right)\)
• D) concave downward on \(\left( - \infty , - \frac { 4 } { 9 } \right) ;\) concave upward on \(\left( - \frac { 4 } { 9 } , \infty \right)\)
• E) concave downward on \(\left( - \infty , \frac { 4 } { 9 } \right) ;\) concave upward on \(\left( \frac { 4 } { 9 } , \infty \right)\)

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Definitions:

Higher Brain Regions

Complex areas of the brain involved in advanced functions such as decision-making, reasoning, and emotional regulation.

Medulla

An area of the brainstem responsible for controlling vital functions like breathing and heart rate.

Cerebellum

A brain structure located at the base of the skull that is involved in coordinating voluntary movements, balance, and posture.

Thalamus

A brain structure that acts as a relay station for sensory and motor signals to the cerebral cortex.