The Function F(x) = Sin $x ^ { 2 }$ Is Approximated by Its Second Taylor Polynomial

Multiple Choice

The function f(x) = sin $x ^ { 2 }$ is approximated by its second Taylor polynomial $\mathrm { P } 2$ (x) at x = 0. Which of the following statements is NOT true?

A) f'(0) = 0
B) $\mathrm { P } 2$ (x) = $\frac { 1 } { 3 }$ + $x ^ { 2 }$
C) $\mathrm { P } 2$ (x) = $x ^ { 2 }$
D) f''(0) = 2
E) none of these