Estimate the value of $\sqrt[3]{11}$ by using three iterations of Newton's method to solve the equation $x^{3}-11=0$ with initial estimate $x_{0}=2 \text {. }$ Round your final estimate to four decimal places.
A) 3.3166
B) 2.253
C) 3.2605
D) 2.224

Question

Quizplus · Accepted Answer

Newton's method formula is $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$. For $f(x) = x^3 - 11$, $f'(x) = 3x^2$. Starting with $x_0 = 2$, the iterations are: $x_1 = 2.8333$, $x_2 = 2.2796$, $x_3 = 2.2240$. Rounding $x_3$ gives 2.224.

Estimate the Value Of 113\sqrt[3]{11}311​ By Using Three Iterations of Newton's Method to Solve the Newton's

Estimate the Value Of $\sqrt[3]{11}$ By Using Three Iterations of Newton's Method to Solve the Newton's