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

question 121

Essay

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.
- $\text { The function } \mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } + \frac { 200 } { \mathrm { x } } , 0 < \mathrm { x } < \infty$ models the perimeter of a rectangle of dimensions x by $\frac{100}{x}$
(a) Find the extreme values for P.
(b) Give an interpretation in terms of perimeter of the rectangle for any values found in part (a).

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