Approximate the zero(s) of the function. Use Newton\'s Method and continue the p

Question

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. Newton's method: Graphing utility: Need Help?Read ItWatch It Talk to a Tutor -11 points LarCalc10 38.008 My Notes Ask Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. Newton's method: Graphing utility: Need Help?Read ItWatch It Talk to a Tutor

Explanation / Answer

f = x^3 + x - 3
f'= 3x^2 + 1

Start x0 = 1
f(1) = -1
f'(1) = 4

So, x1 = x0 - f(x0)
x1 = 1 + 1/4 = 1.25

x1 = 1.25

Now, f(1.25) = 1.25^3 + 1.25 - 3 = 0.203125
f'(1.25) = 5.6875

Now, x2 = 1.25 - 0.203125/5.6875
x2 = 1.214

Now, f(1.214) = 0.003188344
f'(1.214) = 5.421388

Now, x3 = 1.214 - 0.003188344/5.421388
x3 = 1.213

So, newtons method :
1.213

Graphing calc :
1.213

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Same way this one....

Newtons : 1.359

GC : 1.359

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