Find Intervals where function is increasing and decreasing

[Guest]

I'm having a problem determining how to find increasing and decreasing points with out using the graphing calculator.

Example:
2t/t^2+1

I know that I need to take the derivative which = t(t-4)/(t^2+t)^2 after using the quotient rule. I then set the derivative = 0 and come up with t=0 or t=4. At this point I get stuck and can only get the answer by graphing the original function. Even then, I have trouble reading the answer from the graph.

Can someone tell me if I am on the right track and what the graph of the function looks like?

Thanks

 

[tkhunny]

First, you had better check that derivative again.

You can simply evaluate the derivative and see the sign of what you get. For example, f(t) = t² - 1

We have f'(t) = 2*t -- This is relatively obviously positive (f(t) is INcreasing) for t > 0 and negative (f(t) is DEcreasing) for t < 0

 

[Guest]

Thank you. I figured out my error in finding the derivative (I wrote the problem wong).

Here are my steps:

2t/t^2+1

Using quotient rule to find derivative, I get:
(t^2+1)(2)-(2t)(2t) = 2t^2+2-4t^2/(t^2+1)^2

-2t^2 +2 = -2(t^2 - 1)/(t^2+1)^2