For which of the initial approximations $ x_1 = a $, $ b $, $ c $, and $ d $ do you thing Newton's method will work and lead to the root of the equation $ f(x) = 0 $?
$a, b,$ or $c$ will likely work
We know that when X one equals d, the tangent line intersects with the X axis far off to the left not particularly close. Therefore, we know that X two intersex the X axis further away to the right. Therefore, we know Newton's method would failed for this initial approximation there for a being C will work. However, we already established why d may not work given New Newton's method.