Question

Consider the following equation:
f(x)=x^3+〖4x〗^2-10=0
with a root in the interval [1, 2] approximating the root of f at 0.0005 tolerance level,solve for Newton method

Answer 1

My guess is, find f(1.5)
See whether the sign of f(x) changes between f(1) and f(1.5) or between f(1.5) and f(2).
Whichever interval changes, then find f(x) at the midpoint of that interval and repeat the process until you find the root to the desired decimal place.

Answer 2

f(x) = x^3+4x^2-10
f(1) = 1 + 4 - 10 = -5
f(2) = 8 + 16 - 10 = 14
The sign of f(x) changes between 1 and 2 and therefore there is a root between 1 and 2.
Take the midpoint of the interval: (1+2)/2 = 1.5
Find f(1.5)
f(1.5) = (1.5)^3 +4(1.5)^2 - 10 = +2.375
sign changes between 1 and 1.5.
choose the midpoint: (1+1.5)/2 = 1.25
Find f(1.25) and repeat the process