Use Newton's Method to find the x-coordinate of the intersection of y = x⁴ + 2x³ and y = 2x² + 2x + 1. A) 2.2567568 B) 1.7495299 C) 1.4423189 D) 1.3057137 E) 1.2762086

Question

Quizplus · Accepted Answer

To find the x-coordinate of the intersection of the two given functions, we first set them equal to each other and then solve for x. The given functions are $y = x^{14} + 2x^{13}$ and $y = 2x^{12} + 2x + 1$. Setting them equal to each other gives us the equation $x^{14} + 2x^{13} = 2x^{12} + 2x + 1$. To solve this using Newton's Method, we need to rearrange it to $0 = x^{14} + 2x^{13} - 2x^{12} - 2x - 1$ and then apply Newton's Method, which requires an initial guess and the use of the derivative of the function for iteration. The correct answer, after applying Newton's Method with appropriate initial guesses and iterations, leads to the x-coordinate of the intersection, which is closest to 1.2762086.

Use Newton's Method to Find the X-Coordinate of the Intersection