Find the Value or Values Of $c$ That Satisfy the Equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$

question 1

Multiple Choice

Find the value or values of $c$ that satisfy the equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$ in the conclusion of the Mean Value Theorem for the function and interval.
- $f ( x ) = \tan ^ { - 1 } x , \left[ - \frac { \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right] \quad$ Round to the nearest thousandth.

• A) \(0.320\)
• B) \(0,0.320\)
• C) \(- 0.320,0,0.320\)
• D) \(\pm 0.320\)

---

Definitions:

PhD Degree

The highest academic degree awarded by universities in most fields of study, signifying mastery of a particular subject area or field of research.

Psychology

The scientific study of the mind and behavior, encompassing various aspects of conscious and unconscious experience as well as thought.

Decriminalization

The reduction or elimination of legal penalties for certain acts, previously considered criminal offenses, without making the act legal.

Longitudinal Research

A method of study that follows the same participants over a period of time to observe changes or development.