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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Definitions:

PTH

Parathyroid Hormone (PTH) is a hormone secreted by the parathyroid glands that regulates calcium levels in the blood.

Bone

Bone is a durable connective tissue comprised of collagen, calcium, and other minerals, forming the skeletal structure that supports and protects the body's organs and allows movement.

Kidneys

Vital organs responsible for filtering waste products from the blood and excreting them in urine, regulating electrolyte levels, and managing blood pressure.

Muscle

A tissue composed of fibers capable of contracting to produce movement in parts of the body.