Let F(x) = $e ^ { x / 2 }$ Determine the Second Taylor Polynomial of F(x) at X

Multiple Choice

Let f(x) = $e ^ { x / 2 }$ . Determine the second Taylor polynomial of f(x) at x = 2.

A) 1 + $\frac { 1 } { 2 }$ (x - 2) + $\frac { 1 } { 8 }$ $( x - 2 ) ^ { 2 }$
B) 1 - $\frac { 1 } { 2 }$ (x - 2) + $\frac { 1 } { 8 }$ $( x - 2 ) ^ { 2 }$
C) 1 + $\frac { 1 } { 2 }$ (x - 2) + $\frac { 1 } { 6 }$ $( x - 2 ) ^ { 2 }$
D) e + $\frac { \mathrm { e } } { 2 }$ (x - 2) + $\frac { \mathrm { e } } { 8 }$ $( x - 2 ) ^ { 2 }$