Use Newton's Method to approximate the zero(s) of the function $f ( x ) = x - 2 \sqrt { x + 1 }$ accurate to three decimal places.
A)4.828
B)4.832
C)-4.828
D)-4.832
E)4.822

Question

Quizplus · Accepted Answer

Newton's Method uses the formula $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ to iteratively find the roots of a function. First, we need to find the derivative of $f(x) = x - 2\sqrt{x + 1}$. The derivative, $f'(x) = 1 - \frac{1}{\sqrt{x + 1}}$. Choosing a reasonable starting point, such as $x_0 = 4$, and applying the formula iteratively, we converge to the root $x \approx 4.828$, accurate to three decimal places.

Use Newton's Method to Approximate the Zero(s) of the Function f(x)=x−2x+1f ( x ) = x - 2 \sqrt { x + 1 }f(x)=x−2x+1​

Use Newton's Method to Approximate the Zero(s) of the Function $f ( x ) = x - 2 \sqrt { x + 1 }$