Find All Value(s) of C (If Any) That Satisfy the Conclusion

question 72

Multiple Choice

Find all value(s) of c (if any) that satisfy the conclusion of the Mean Value Theorem for the function $f ( x ) = \frac { 1 } { 1 + x }$ on the interval $[ 0,1 ]$ .

• A) \(\frac { 1 } { 2 }\)
• B) \(\frac { 1 } { \sqrt { 2 } }\)
• C) \(\frac { 1 } { 4 }\)
• D) \(- \frac { 1 } { 4 }\)
• E) \(\sqrt { 2 } - 1\)
• F) \(2 - \sqrt { 2 }\)
• G)0
• H)No value

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Definitions:

Client-centered Therapy

A counseling approach where the therapist provides a supportive environment to allow the client to lead the process of therapy.

Carl Rogers

An influential American psychologist who founded the client-centered therapy approach, emphasizing the importance of an individual's self-view and the need for unconditional positive regard.

Developed

A state of growth or advancement, often in the context of countries, technology, or individual skills.

Humanistic Therapies

A category of psychotherapy that emphasizes personal growth and self-fulfillment, focusing on the patient's individual viewpoint as a key to psychological health.