Let $f ( x ) = x + \frac { 1 } { x } f$

Multiple Choice

Let $f ( x ) = x + \frac { 1 } { x } f$ on $\left[ \frac { 1 } { 2 } , 2 \right] .$ Then the set of all c in $\left( \frac { 1 } { 2 } , 2 \right)$ guaranteed by the Mean Value Theorem is

A) $\left\{ \frac { 3 } { 4 } \right\}$
B) $\{ 1 \}$
C) $\left\{ \frac { 5 } { 4 } \right\}$
D) $\left\{ \frac { 3 } { 2 } \right\}$
E) $\left\{ \frac { 7 } { 4 } \right\}$