Thread: Find MINs, MAXs, POI and concavity...HELP!

I already asked for help in another Thread I posted. Please help me out.

I'm having problems with solving for X inhere...

y'=
- 2cos(x/(x-2))
(x-2)^2


now I have to set it equal to zero and solve for X.

0=- 2cos(x/(x-2))
(x-2)^2

what are the possible values for X? by the way, my domain is from 0 to 2pi.

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.

So you have
0 = -2cos[x / (x-2)] / (x-2)^2

Continue simplifying that.
0 = -2cos[x / (x-2)]
0 = cos[x / (x-2)]
angle [x / (x-2)] = arccos(0) = pi/2 or 3pi/2 ---***

When [x /(x-2)] = pi/2,
Cross multiply,
2x = (x-2)pi
2x = pi(x) -2pi
x(2 -pi) = -2pi
x = 2pi / (pi-2) = 5.50387679 radians -------answer.

When [x /(x-2)] = 3pi/2,
Cross multiply,
2x = (x-2)3pi
2x = 3pi(x) -6pi
x(2 -3pi) = -6pi
x = 6pi / (3pi-2) = 2.5387366 radians -------answer also.