Math Problem Statement

use newton's method to estimate the two zeros of the function f(x) = x^4 - 2x - 2. Start with x0 = 1 for the zero on the right. then in each case, find x2.

Determine x2 when x0 = -1

x2= ____ type an integer or a simplified fraction

Then determine x2 when x0 = 1

x2 = ____ type an integer or a simplified fraction

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Numerical Methods
Root Finding
Newton's Method

Formulas

Newton's Method Formula: x_(n+1) = x_n - f(x_n) / f'(x_n)
Derivative of f(x) = x^4 - 2x - 2: f'(x) = 4x^3 - 2

Theorems

Newton's Method for Root Approximation

Suitable Grade Level

Grades 11-12 or College