Use Newton's Method to Approximate the Indicated Root Of $x ^ { 4 } + x - 4 = 0$

Short Answer

Use Newton's method to approximate the indicated root of $x ^ { 4 } + x - 4 = 0$ in the interval $[ 1,2 ]$ , correct to six decimal places.
Use $x _ { 1 } = 1.5$ as the initial approximation.