A Polynomial F(x) of Degree 3 for Which F(1) = $\frac { 1 } { 2 }$

Multiple Choice

A polynomial f(x) of degree 3 for which f(1) = -1, f'(1) = 2, f''(1) = -1, and f'''(1) = -2 is given by

A) f(x) = -1 + 2(x - 1) - $\frac { 1 } { 2 }$ $( x - 1 ) ^ { 2 }$ - $\frac { 1 } { 3 }$ $( x - 1 ) ^ { 3 }$
B) f(x) = -1 + 2(x - 1) - 1 $( x - 1 ) ^ { 2 }$ - 2 $( x - 1 ) ^ { 2 }$
C) f(x) = -1 + 2x - $x ^ { 2 }$ - 2 $x ^ { 3 }$
D) f(x) = $x ^ { 3 }$ - 2 $x ^ { 2 }$ - 3x + 2
E) none of these