# Thread: intervals inc and dec and local min/max

1. ## intervals inc and dec and local min/max

Missed class and starting homework. Need a quick walk through and I think I can figure out the rest of the problems.

f(x)= (8x)/((x^2)+4)

a) find the intervals on which f(x) is increasing.
b) find the intervals on which f(x) is decreasing
c)find the local maximum and local minimum points (x & y values)

2. Well to find the critical points of the function who take the first derivative of the function you were given, lets call it $f(x)$ in this case, and you solve the derivative by solving it when it is equal to 0. Once you have the critical points of the function you can find the maxima and minima by plugging it into the original function also also dont forget to test the end points If your given a certain integral, also If I recall to determine if the function is increasing, I might be mistaking concavity for this but simple make a number line with the critical points and simply plug some number small and bigger than each critical point to see if its increasing or decreasing on some interval as x increases.

3. So I start out by getting the first derivative of the function, which I got:

((8x^2)-16x+32)/((x^2)+4)^2

Starting on rest. Hoping that's right.

4. Yes, that looks correct, now find the critical points

5. So I replace x with 0 and get 2. Or am I suppose to try and make the function equal 0 or undefined? I can't make the bottom portion equal zero so I know that it isn't undefined. So how do I make the top equal to 0, everything I try seems to get me close, but not there.