For the Function : (A) Find the Critical Numbers

question 4

Multiple Choice

For the function : (a) Find the critical numbers of f (if any) ;
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.
Then use a graphing utility to confirm your results.

• A) (a) x = 0 , (b) increasing: ; decreasing: (c) relative max: ; relative min:
• B) (a) x = 0 , (b) decreasing: ; increasing: (c) relative min: ; relative max:
• C) (a) x = 0 , (b) increasing: ; decreasing: (c) relative max: ; no relative min.
• D) (a) x = 0 , (b) increasing: ; decreasing: (c) relative max: ; relative min:
• E) (a) x = 0 , (b) decreasing: ; increasing: (c) relative min: ; relative max:

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Definitions:

Stressors

External pressures or stimuli that can cause stress, affecting an individual's emotional and physical well-being.

Unpleasant Life Events

Events or occurrences in one's life that cause distress, discomfort, or unhappiness.

Positive and Negative Effects

Refers to the beneficial or harmful outcomes that result from actions, processes, or conditions, impacting various aspects of life or the environment.

Depression

A mental health disorder characterized by persistently depressed mood or loss of interest in activities, causing significant impairment in daily life.