Question

Using Newton-Raphson method to solve $f(x) = e^{-x} - x$ with initial guess $x_0 = 0$, find the next iteration.

• A. 0.56
• B. -0.50
• C. 0.50
• D. -0.56

Hint:

Newton-Raphson requires function and derivative at a guess point. Formula: $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

Answer 1

The Correct Option is C

Step 1: Newton-Raphson Formula 
\[ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \] Step 2: Compute at $x_0 = 0$ 
\[ f(x) = e^{-x} - x, f(0) = 1 - 0 = 1 \] \[ f'(x) = -e^{-x} - 1, f'(0) = -1 - 1 = -2 \] \[ x_1 = 0 - \frac{1}{-2} = 0.5 \]