Use Newton's Method to approximate the solutions of x⁴- 77 = 0. Use 4 for your initial value and calculate four iterations. A) -3.0108653, 3.0108653 B) -2.9634212, 2.9634212 C) -2.9622573, 2.9622573 D) -3.300781, 3.300781 E) -4, 4

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Quizplus · Accepted Answer

Using Newton's Method, we have: $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ where $f(x)=x⁴ F1F1F1S1-F1F1F10$ and $f'(x)=(⁴F1F1F1S1)'=⁴F1F1F1$ Starting with $x_0=4$: $x_1=4-\frac{4⁴F1F1F1S1-F1F1F10}{⁴F1F1F1}=2.9623623$ $x_2=2.9623623-\frac{2.9623623⁴F1F1F1S1-F1F1F10}{⁴F1F1F1}=-2.9622573$ $x_3=-2.9622573-\frac{-2.9622573⁴F1F1F1S1-F1F1F10}{⁴F1F1F1}=2.9622573$ $x_4=2.9622573-\frac{2.9622573⁴F1F1F1S1-F1F1F10}{⁴F1F1F1}=-2.9622573$ Therefore, the solution is $x=-2.9622573$ and the answer is C.

Use Newton's Method to Approximate the Solutions of X4- 77

Use Newton's Method to Approximate the Solutions of X⁴- 77