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Let f(x)= x^3 -2x-2...Newton-Raphson type question??
Find an interval of the form [n,n+1] such that f is guaranteed to have a zero c in [n, n+1], and give a reason for your choice.
Also, from your value of n in the first part, let c1=n. Then use the Newton-Raphson method to find c2.
Thanks a lot.
1 Answer
- 5 years ago
f'(x) = 3x^2 - 2
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = ±sqrt(2/3)
x = sqrt(2/3) - min; x = -sqrt(2/3) - max
f(-sqrt(2/3)) = -0.911 < 0
f(sqrt(2/3) = -3.089 < 0
lim(x->+oo)f(x) = +oo =>f(2) = 2>0 => f(x) = 0 x ϵ [sqrt(2/3), 2]
c1 = sqrt(2/3)
