Originally Posted by

**maksim378** After I did the 1st derivative test, I had to find MINs, MAXs, POI as I said before.

to find the critical value, I have to find the answer for X in the derivative (that was my last question).

let's say that the answer for X was 2, lets imagine.

then we'd have to do the line test where I'd put the point (2) on the line and choose any other points around:

1 **2** 3

then I'd plug those other 2 numbers (1 and 3) into the derivative. the answer would give me an idea of how the graph looks like. when I plug in 1 into the derivate, let's sa taht the answer is positive and for 3, it's positive also

so those signs help me out on the number line

__+++ +++__

1 2 3

if the line was -----+++++ then it's a MIN, if it was ++++----, then it's a MAX, if the line is --- --- or +++ +++ then that's a POI.

then I'd plug the answer for X that we've found in the derivative (**2**) into the original equation and that woul give me the Y coordinate. so now I have the X which is 2 and the Y coordinate. now I now the coordinates of a point which happened to be our Poin Of Inflection.

that's what I'd do with an easy problem. in the one I have, we had to put N in order to solve for X. N is any number, then the answer for X will be different everytime... then I won't be able to find MIN or MAX or POI coordinates... or is there a way to do that?

P.S. btw, the answer for X in my real derivative -2cos(x/(x-2))/(x-2)^2 can't be 0, I figure that out. I hope Im at least right in this case.