The Function $f(x)=e^{-\frac{x}{7}}$ Satisfies the Hypotheses of the Mean Value Theorem on the Theorem

question 56

Multiple Choice

The function $f(x) =e^{-\frac{x}{7}}$ satisfies the hypotheses of the Mean Value Theorem on the interval $[0,14] .$ Find all values of c that satisfy the conclusion of the theorem.

• A) \(-7 \ln \left(\frac{e^{2}-1}{2 e^{2}}\right)\)
• B) \(7 \ln \left(\frac{e^{2}-1}{7 e^{2}}\right)\)
• C) \(-7 \ln \left(\frac{e^{2}-1}{7 e^{2}}\right)\)
• D) \(7 \ln \left(\frac{e^{2}-1}{2 e^{2}}\right)\)

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