Kaylin C.
asked • 10/30/21Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 8 = 0.
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1 Expert Answer
I assume you mean x4 - x - 8:
Newton's method: xn+1 = xn - f(xn)/f'(xn)
x1 = 1 find f(1) and take the derivative to find f'(1) and plug in for n=1. Your new x value (x2) should have an f(x) closer to zero.
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Kaylin C.
can you answer this for me? i keep getting it worng
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10/30/21
Kaylin C.
wrong*
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10/30/21
JACQUES D.
tutor
f'= 4x^3-1 f(1) =-8 f'(1)=3
X2 = 1 + 8/3 = 11/3. This overshoots the zero quite a bit, but it starts doing better if you keep going. If you start at 2, NM works really fast.
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10/30/21
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Kaylin C.
Round answer to 4 decimal places10/30/21