use newtons method with the initial approximation x1 1 to f

use newton\'s method with the initial approximation x₁ = 1 to find x_2, the second approximation to the root of the equaltion X⁴-X-1=0. explain how the method works by first graphing the function and its tagen line at (1,-1). show work

Solution

f(x) = x x 1
f \'(x) = 4x³ 1

x = x f(x)/f\'(x) = x (x x 1)/(4x³ 1)

x = 1
x = 1 f(1)/f\'(1) = 1 (111)/(41) = 1 1/3 = 4/3