Find the Value or Values Of $c$ That Satisfy the Equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$

question 75

Multiple Choice

Find the value or values of $c$ that satisfy the equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$ in the conclusion of the Mean Value Theorem for the function and interval.
- $$f ( x ) = x + \frac { 18 } { x } , [ 2,9 ]$$

• A) 2,9
• B) \(3 \sqrt { 2 }\)
• C) \(0,3 \sqrt { 2 }\)
• D) \(- 3 \sqrt { 2 } , 3 \sqrt { 2 }\)

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Definitions:

Periosteum

A dense layer of vascular connective tissue enveloping the bones except at the surfaces of the joints.

Diaphysis

The main or central shaft of a long bone.

Articular Cartilage

The smooth, white tissue that covers the ends of bones where they come together to form joints, facilitating smooth movement.

Metaphysis

The narrow portion of a long bone between the epiphysis and the diaphysis involved in growth during childhood.