Consider a Continuous Function with the Following Properties $f(0)=4$ $\left|f^{\prime}(x)\right|<0.5$ $f^{\prime \prime}(x)<0$

question 87

Multiple Choice

Consider a continuous function with the following properties: $f(0) =4$ $\left|f^{\prime}(x) \right|<0.5$ $f^{\prime \prime}(x) <0$ for $x<0$ $f^{\prime}(1) =0$ . Which of the following is true?

• A)The graph must have a local maximum for \(x<0\) .
• B)The graph must not have a local maximum for \(x<0\) .
• C)The graph may or may not have a local maximum for \(x<0\) .

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Definitions:

Endorphins

Neurotransmitters produced by the body to relieve pain and stress, often associated with feelings of euphoria.

Prolonged Stress

Extended exposure to stressful situations or stimuli, which can have negative long-term effects on health and well-being.

Aerobic Exercise

Physical activity that improves cardiovascular health by increasing the heart rate and maximizing the amount of oxygen in the blood.

Stress-Moderating Hormone

Hormones that play a role in the body's response to stress, helping to regulate or moderate the stress response.