Need calculus help with Newton's Method Problem

timer Asked: Dec 7th, 2015
account_balance_wallet $5

Question Description

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.

Tutor Answer

School: University of Virginia

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. :)

flag Report DMCA

Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

Similar Questions
Hot Questions
Related Tags
Study Guides

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors