Use Newton's method to find the root of $6 x ^ { 3 } - x ^ { 2 } - 19 x + 6 = 0$ that lies between 0 and 1.
A)0.316
B)0.333
C)0.158
D)0.167
E)0.474
F)0.500
G)0.079
H)0.084

Question

Quizplus · Accepted Answer

Newton's method is an iterative numerical technique. Starting with an initial guess, say $x_0 = 0.5$, and using the derivative $f'(x) = 18x^2 - 2x - 19$, the iterations converge to approximately 0.333, which is the root between 0 and 1.

Use Newton's Method to Find the Root Of 6x3−x2−19x+6=06 x ^ { 3 } - x ^ { 2 } - 19 x + 6 = 06x3−x2−19x+6=0

Use Newton's Method to Find the Root Of $6 x ^ { 3 } - x ^ { 2 } - 19 x + 6 = 0$