i) Consider the following function: f(x)  = 3 + 6x + 5x2 + 3x3 + 4x4. Locate the minimum by finding the root of the derivative of this function. Use bisection with initial guesses of xl = -2 and xu = 1. ii) Determine if the equation f(x) = x3 - 3 in the interval [ 1,2 ] can be solved using the Bisection method. iii) Approximate the root of the equation in the interval given using the Bisection in ii) above to a relative error of 0.1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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i) Consider the following function:

f(x)  = 3 + 6x + 5x2 + 3x3 + 4x4.

Locate the minimum by finding the root of the derivative of this function. Use bisection with initial guesses of xl = -2 and xu = 1.

ii) Determine if the equation f(x) = x3 - 3 in the interval [ 1,2 ] can be solved using the Bisection method.

iii) Approximate the root of the equation in the interval given using the Bisection in ii) above to a relative error of 0.1.

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