Employ the Newton-Raphson method to determine a real root for f(x) = -2 + 6x - 4x^2 + 0.5x^3 using initial guesses of (a) 4.2 and (b) 4.43.
Added by Lourdes D.
Step 1
Given: \[ f(x) = -2 + 6x - 4x^2 + 0.5x^3 \] Calculate the derivative \( f'(x) \): \[ f'(x) = \frac{d}{dx}(-2 + 6x - 4x^2 + 0.5x^3) \] \[ f'(x) = 6 - 8x + 1.5x^3 \] Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 73 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The polynomial function f(x) = -1 + 5.5x - 4x^2 + 0.5x^3 has a real root between 0 and 1. Apply the Newton-Raphson method to this function using an initial guess of x0 = 4.52. Repeat using an initial guess of x0 = 4.54. Explain your results.
Madhur L.
Find the root of the equation from: f (x) = x3 - 6x^2 - 24x + 64 a) By the bisection method (two iterations, xl = 0, xu = 3) b) By the false-position method (two iterations, xl = 0, xu = 3) c) With the Newton-Raphson method (two iterations, xi = 1.5) d) By the Secant method (two iterations, xi-1 = 0, xi = 1.5)
Adi S.
Use secant method with initial guesses x0=3 and x1=4 to find the value of the root in the second iteration for the function f(x) = 2 x^3 -3 x^2+x - 6 2.2 2.8 2 2.3
Sri K.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD