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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The Answer of 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) $7 \ln \left(\frac{e^{2}-1}{2 e^{2}}\right)$

The Function f(x)=e−x7f(x)=e^{-\frac{x}{7}}f(x)=e−7x​ Satisfies the Hypotheses of the Mean Value Theorem on the Theorem

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