Answer
$x_2\approx1.19$
Work Step by Step
Step 1. Given $f(x)=x^4-2$, we have $f'(x)=4x^3$.
Step 2. Use Newton’s method $x_{n+1}=x_n-\frac{f(x)}{f'(x)}$ to estimate the solution up to $x_2$.
Step 3. Start with $x_0=1$; we can get the result $x_2\approx1.19$ as shown in the table.
