The Newton-Raphson algorithm is used to approximate the zero of f(x) = $x ^ { 3 }$ + x - 5 between x = 1 and x=2 . If x₀= 1, find x₁. A) 7/4 B) 1/4 C) 3/4 D) 7/3 E) none of these

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The Newton-Raphson formula is $$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$$Given $$f(x) = x^3 + x - 5, \ \ \ f'(x) = 3x^2 + 1$$and $$x_0 = 1$$So, $$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 1 - \frac{1^3 + 1 - 5}{3(1)^2 + 1} = 1 - \frac{-3}{4} = \frac{7}{4}$$

The Newton-Raphson Algorithm Is Used to Approximate the Zero of F(x)