Let f(x) be the Taylor Polynomial P_7(x) of order 7 of arctan(x) about x=0. Then it follows that, if -1.5<x<1.5,

A) f(x) = arctan(x)

B) f(x) </= arctan(x)

C) f(x) >/= arctan(x)

D) f(x) > arctan(x) if x < 0, but f(x) < arctan(x) if x > 0

E) f(x) < arctan(x) if x < 0, but f(x) > arctan(x) if x > 0

my book says the answer is D) but i have no idea how they figured out whether or not f(x) is greater than arctan(x). please help.