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:

Faulty Parallelism

A grammatical inconsistency in a sentence where parts that are meant to be parallel in structure do not match in form.

Mixed Construction

A sentence structure that improperly mixes elements, making it confusing or grammatically incorrect.

Incomplete Construction

Refers to a structure or project that has not been finished, often due to various constraints like funding or time.

Dangling Modifier

A term or expression that alters the meaning of an unspecified word within a sentence, typically resulting in uncertainty or obscurity.