Question

Find the critical numbers, find the open intervals on which the algebraic function is increasing or decreasing, and locate all relative extrema. Function: (x+3)/x^2
Can someone go through all of the steps to do this, please?

Answer 1

1. Find the derivative
2. Find the critical points by:
2a) Find when the derivative =0
2b) Find when the derivative doesn't exist
3. Place the critical points on a sign diagram
4. Plug in numbers in between the critical points into the derivative. If you get a positive value, then it's inceasing on that interval. If you get a negative value, then it's decreasing on that interval.

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtI.aspx

Check out example 1 if you want

Answer 3

Thanks, haha! But I know how to do it, in theory I suppose, it's just where I'm executing it that I'm having problems. I have found the critical numbers (I think) as 0 and -6, and I've found it (I think) decreases from -infinity to -6, increases from -6 to 0, and decreases again from 0 to infinity. It's just these numbers don't seem to work to plug in to get the maximum/minimum, I keep getting numbers over zero and you can't divide by zero or the universe will implode, haha.

Answer 4

Sorry I had to go yesterday. Yup, the critical numbers are 0 and -6!

0 is a critical number, but it's not a local extrema, because it doesn't exist in the original function. That's why you're getting a division by 0. So the only local extrema is at -6. You can check this type of stuff on WolframAlpha: http://www.wolframalpha.com/input/?i=%28x%2B3%29%2Fx%5E2.

You can see that on the graph that your intervals of increasing decreasing/increasing are correct, good job!