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