Answer
a) $x_2\approx 7.3$, $x_3\approx6.8$.
b) Yes.
Work Step by Step
a) The tangent line at $x_1$ = $6$ intersects the $x$-axis at $x$ $\approx$ $7.3$, so $x_2$ = $7.3$.
The tangent line at $x$ = $7.3$ intersects the $x$-axis at $x$ $\approx$ $6.8$, so $x_3$ $\approx$ $6.8$.
b) $x_1$ = $8$ would be a better first approximation because the tangent line at $x$ = $8$ intersects the $x$-axis closer to $s$ than the first approximation $x_1$ = $6$.
