using newton method find the approximate root for the following equation.

Question

f(x) = x² -12

Answer 1

0 = x^2 -12

x^2 = 12

x = + or - sqr12 = + or - 2sqr3 = + or - 2(1.732) =about + or - 3.464

That's what you'd get with a calculator for sqr12 to 3 decimal places

Newton's Method involves the derivative or f'(x) = 2x

then calculate your best guess - f(x)/f'(x)

guess 4 then f(x) - f(x)/f'(x) = 4 - (16-12)/2(4) = 4-4/8 = 3.5

do it again with x=3.5 instead of 4

f(x) - f(x)/f'(x) = 3.5 - (12.25-12)/7 = 3.5 - .25/7 = 3.5 - 1/28 = 3.464 which is the same as the actual value rounded to 3 decimal places