You are here:

Calculus/Calculus Differentiation and percentage rate of change?

Advertisement

Expert: - 10/7/2011


Question
In each of these cases, find the percentage rate of change of the function f(t) with respect to t at the given value of t. Please show how you got the answer. Thanks!

a) f(t)=t^2(3-2t)^3 at t=1

b) f(t)=(1)/(t+1) at t=0

Answer
a) If the function is f(t) = (t²)(3-2t)³, then this is f(t) = a(t)b(t).
The derivative is f'(t) = a(t)b'(t) + a'(t)b(t).
It is known that a(t) = t², b(t) = (3-2t)³, a'(t) = 2t, and b'(t) = 3[(3-2t)²](-2) = -6(3-2t)².

b) If f(t) = 1/(t+1), this can be rewritten as f(t) = (t+1)^-1.
It can then be seen that f'(t) = -(t+1)^-2, which is the same as f'(t) = -1/(t+1)².

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.