You are here:

Calculus/Maximum or Minimum

Advertisement

Expert: - 10/12/2009


Question
Hi again ... I have another question for you. I can't remember now If I asked you this or not ...

Find the maximum OR minimum of x^4/4 (a fraction, x^4 over 4), + x^3 + 3/2x^2 (3/2 is a fraction) + y.

Thanks
Felipe

Answer
So the equation "x^4/4 (a fraction, x^4 over 4), + x^3 + 3/2x^2 (3/2 is a fraction) + y"
is really "(x^4)/4 + x^3 + 3(x^2)/2 = y"?

The derivative is then y' = x^3 + 3x^2 + 3x.

Note that an x can be factored out, giving y' = x(x² + 3x + 3).

One place to check is at x = 0.  The other is where x² + 3x + 3 = 0.
Using a=1, b=3, c=3, use the quadratic equation, which is (-b±√(b²-4ac))/(2a).

The second derivative at these points will be negative at a maximum,
positive at a minimum, and zero at an inflection point.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.