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newton's method!!!?
Let f(x) = 2x^3 - 9x^2 + 12x -2. Then
a) Show that f(x) = 0 has a root between x = 0 and x = 1.
b) Use the Newton-Raphson method to find the zero of f with x0 = 0. (Find the root in the precision
of 4 decimal places)
1 Answer
- ?Lv 77 years agoFavorite Answer
a) f(0) = -2
f(1) = +3
f ' (x) = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x-1)(x-2), which exists.
So, Intermediate Value Theorem tells us there exists a point c in [0, 1] where f(c) = 0.
b) x1 = x0 - f(x0) / f ' (x0)
Let x0 = 0.5. The x1 = 0.5 - f(0.5) / f ' (0.5)
Wash-Rinse-Repeat
