Question

If you apply Newton's method to f(X)= x³-x-1 with initial value x=1, what will be the next approximation x1? ​

Answer 1

X=1

APPROXIMATIONx1

answer is yes

Answer 2

Answer:

What is the Apy Newton-Raphson method to find a real root of x3+x-1=0?

Find the roots of x3+x−1=0 using the Newton-Raphson method.

Find Initial Estimates for Roots

The Newton-Raphson method iterates and approaches one root. The cubic polynomial here has up to three roots to find.

f(x)=x3+x−1

f′(x)=3x2+1

The first derivative has x2 and the slope is always positive for this curve. The curve should only cross the x-axis once, i.e. one root.

x=(−1)⇒f(−1)=(−3)

x=0⇒f(0)=(−1)

x=+1⇒f(1)=1

The samples indicate the root occurs somewhere on the interval [0,1] . This means x=+1 is a good initial guess.

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Step-by-step explanation:

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