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:

Clamping

The process of holding or securing objects tightly together using a device to prevent movement or separation.

Grasping

The action of seizing or holding firmly, often used to describe the development of motor skills in infants or for understanding concepts.

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Tools consisting of two blades joined together, used for cutting paper, cloth, or other materials.

Cutting

A form of self-injury where individuals intentionally cut their skin as a way of coping with emotional pain, stress, or distress.