You are here:

Calculus/AP calculus

Advertisement

Expert: - 3/13/2008


Question
I have had previous experience in Calculus but have not done any maths for a few years now and cannot remember how to answer this question. Your help is appreciated.

T = 0.001*t^3 + 0.008*t^2 + 0.016*t + 0.5

0 < t < 6
a) What is the domain of T?
b) For what values of t is T increasing and for what values decreasing?
c) What is the smallest value of T in its domain, and when does it occur?

Thx

Answer
Remember that the derivative of x^n is nx^(n-1) and proceed from there.  

In the domain, find the end point values and the max and min.  The function varies between the maximum and minimum values of all of these values of T.  Finding max and min is mentioned in the next paragraph.

To find where T is increasing/decreasing, find the derivative and set it to 0.  Once this has been done, look at the intervals between the 0 values to see whether it is positive (function is increasing) or negative (function is decreasing).  Note that the values only need to be looked at between 0 and 6.

Check and values where the derivative is 0 and the values t=0 and t=6 to find where the minimum is located.

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.