Answer
$x_2\approx-0.32$
Work Step by Step
Step 1. Given $f(x)=x^3+3x-1$, we have $f'(x)=3x^2+3$.
Step 2. Use Newton’s method $x_{n+1}=x_n-\frac{f(x)}{f'(x)}$ to estimated the solution up to $x_2$.
Step3. Start with $x_0=0$; we can get the result $x_2\approx-0.32$ as shown in the table.
