Approximate the Positive Zero(s) of the Function $f ( x ) = x ^ { 3 } - \cos x \text { to three decimal }$

Multiple Choice

Approximate the positive zero(s) of the function $f ( x ) = x ^ { 3 } - \cos x \text { to three decimal }$ places. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. $0.001$

A) $- 0.967$
B) $0.865$
C) $0.842$
D) $- 0.865$
E) $0.916$