The Value for Which Newton's Method Fails for the Function $y = - x ^ { 3 } + 3 x ^ { 2 } - x + 1$

question 63

Multiple Choice

The value for which Newton's method fails for the function below is shown in the graph. Give the reason why the method fails. $y = - x ^ { 3 } + 3 x ^ { 2 } - x + 1$

• A) \(\lim _ { x \rightarrow \infty } \left\{ \begin{array} { l } 0 = x _ { 1 } = x _ { 3 } = \ldots \\ - 1 = x _ { 2 } = x _ { 4 } = \ldots \end{array} \right.\)
• B) \(f ^ { \prime } \left( x _ { 1 } \right) = 0\)
• C) \(f ^ { \prime } \left( x _ { 2 } \right) = 0\)
• D) \(f ^ { \prime \prime } \left( x _ { 2 } \right) = 0\)
• E) \(\lim _ { x \rightarrow \infty } \left\{ \begin{array} { l } 1 = x _ { 1 } = x _ { 3 } = \ldots \\ 0 = x _ { 2 } = x _ { 4 } = \ldots \end{array} \right.\)

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