If F(x) = X(x - 6)² , Find the Intervals

question 490

Essay

If f(x) = x(x - 6)² , find the intervals where f is concave up and where f is concave down.

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Definitions:

Equilibrium

A state of balance or stability, where different elements are in the correct proportions or relation to each other.

Temperature Regulation

The physiological and behavioral processes by which living organisms maintain their body temperature within a certain optimal range, despite external temperature changes.

Hypothalamus

A region of the brain that coordinates the autonomic nervous system and the activity of the pituitary, controlling body temperature, thirst, hunger, and other homeostatic systems, and involved in sleep and emotional activity.

Limbic System

A complex set of brain structures located on both sides of the thalamus, involved in processing emotions, motivation, and memory.