Recall from the solution for part (a) that
We need to solve f ′ ( x ) = 0 {\textstyle f'(x)=0} near x 0 = 1 {\textstyle x_{0}=1} . Using the Hint with f ′ ( x ) {\textstyle f'(x)} in place of F ( x ) {\textstyle F(x)} , we have
Answer: the next approximation is x 1 = 13 12 {\textstyle {\color {blue}x_{1}={\dfrac {13}{12}}}} .