TITLE: Finding Increasing/Decreasing and absolute/local min/max
QUESTION [0 upvotes]: I am kinda confused and feel like I am getting more confused as I dive into these math problems. First, I know that to find critical points(which are needed for increase/decrease and min/max) we take the derivative, and wherever it =0 or =undefined that those are a critical point.
So for example, I have a problem $ \ f(x)=√(25-x^2) \ $ , so $ \ f'(x)= \frac{-x}{\sqrt{25-x^2}} \ $ .
Ok, so that means we have critical points at 0, -5 and 5 correct?
Now by taking these points on intervals (-5,0), (0,5) and seeing where they increase and decrease we can find what we are looking for correct? So on (-5,0) I would say it is decreasing and on (0,5) it is also decreasing correct?
          (Now just a question with the above, when we have 3 critical points, is there a certain number of domain intervals to check for inc/dec? Because I have 3 crit points but 2 domain intervals?)
After this I am stuck. I know that if a function is increasing then decreasing, that will be a local max, and if its decreasing then increasing its a local min. and if there is no change in sign, there is no extreme, so since there is no extreme, is there no global min/max? 
I am kinda stumped, I really need some help with the concept so I can do more of these problems easily.
Thank you

REPLY [1 votes]: Notice that this is
the top half of a circle.
At the endpoints,
the function is vertical,
and in the middle the
function is flat.'
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