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Asked Nov 6, 2019
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2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain
why Newton's method fails. Use x1 = 1 as your initial guess. Continue until successive
approximations differ by less than .001. Show your work
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2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's method fails. Use x1 = 1 as your initial guess. Continue until successive approximations differ by less than .001. Show your work

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Expert Answer

Step 1

Consider the given function,

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f(x)=-x' +3x2 -x+1 initial value x

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Step 2

According to the Newton’s method,

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f (x) = x, 1+1 where,i 0,1, 2,... f (x) f (x) So,x x here,x 1 f (1) 3.12 -1+1 =2 f (x)3x 6x f (1)=-3(1)+6(1)-1 =2 2 =1 2 thus,x =0

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Step 3

The next iteration val...

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f(x) f (x) here,x 0 (-0) 3.02-0+1 0 -3.026.0-1 -1 f(x) f (x) (-1)3.12-1+1 =1- -3.126.1-1 0 f(x.) (x.) (-0)3.02-0 +1 = 0 -3.026.0-1 - 1

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