Need calculus help with Newton's Method Problem

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Let f(x)=x^4-x^3. Show that the equation f(x)=75 has a solution in the interval [3,4] and use Newton’s method to find it. Please show work.

Dec 7th, 2015

Thank you for the opportunity to help you with your question!

We have the function as


We have x^4-x^3=75


Let g(X)=x^4-x^3-75



As the g(3) value is negative and the g(4) value is positive it implies that the function has a solution in the interval in the [3,4] as the graph crosses the x-axis in this interval.

Newtons method to find the solution;

x(n+1)=xn- f(xn)/f'(xn)

Here n=3

x(n+1)=xn -(xn^4-x^n3-75)/(4xn^3-3xn^2)

Let x_0 = 3.5...recursive relation is ( 3 x^4 - 2 x³ + 75 ) / ( 4 x³ - 3 x²)

Using a calculator 5 times the 10 place accuracy...3.2285

I hope this would help you,but if you have any doubt regarding this,you can surely ask. :)
Dec 7th, 2015

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