Sketch the Graph Of $f ( x ) = x ^ { 4 } + x - 3$

Sketch the graph of $f ( x ) = x ^ { 4 } + x - 3$ on the interval $[ - 3,3 ]$ . Suppose that Newton's method is used to approximate the positive root of f with initial approximation $x _ { 1 } = 2$ .(a) On your sketch, draw the tangent lines that you would use to find $x _ { 2 }$ and $x _ { 3 }$ , and estimate the numerical values of $x _ { 2 }$ and $x _ { 3 }$ .(b) To approximate the negative root of f, use $x _ { 1 } = - 2$ as the starting approximation. As before, draw the tangent lines that you would use to find $x _ { 2 }$ and $x _ { 3 }$ , and estimate the numerical values of $x _ { 2 }$ and $x _ { 3 }$ .(c) Suppose that you had used $x _ { 1 } = 0$ as the starting point for approximating the negative root. Discuss what would happen.