Question

The Newton-Raphson method fails for the function $ f(x) $, if

• A. \( f'(x) \) is negative
• B. \( f'(x) \) is too large
• C. \( f'(x) \) is zero
• D. Never fails

Hint:

Always check the derivative when applying the Newton-Raphson method. If the derivative is zero at any point, the method cannot be used at that point.

Answer 1

The Correct Option is C

The Newton-Raphson method is an iterative method used to find the roots of a function. The formula is: \[ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \] For the method to work, \( f'(x_n) \) must not be zero. If \( f'(x) = 0 \), the method fails because division by zero is undefined.
Therefore, the correct answer is 3. \( f'(x) \) is zero.