(Solved): The figure shows the graph of a function \( f \). Suppose that Newton's method is used to approxim ...

The figure shows the graph of a function \( f \). Suppose that Newton's method is used to approximate the root \( s \) of the equation \( f(x)=0 \) with initial approximation \( x_{1}=6 \). (i) (a) Draw the tangent lines that are used to find \( x_{2} \) and \( x_{3^{\prime}} \) and estimate the numerical values of \( x_{2} \) and \( x_{3} \). (Round your answers to one decimal place.) \[ \begin{array}{l} x_{2}= \\ x_{3}= \end{array} \] (b) Would \( x_{1}=8 \) be a better first approximation? Explain. We know that \( x_{1}=8 \) be a better first approximation because the tangent line at \( x=8 \) intersects the \( x \)-axis \( \quad s \) than does the first approximation \( x_{1}=6 \).