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

Question

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).

Quizplus · Accepted Answer

The Answer of  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).

Find the Value or Values Of ccc That Satisfy the Equation f(b)−f(a)b−a=f′(c)\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )b−af(b)−f(a)​=f′(c)

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