What are the critical points of (-2x^2-2)/(x^2-1)^2 ?

Question

babyslapmafro · Answer

First find the derivative

anonymous · Answer

Sorry, that is the first derivative. I need to find the zeroes of that. All I get are imaginary numbers.

babyslapmafro · Answer

Oh ok, one moment...

babyslapmafro · Answer

Yes, same here, imaginary number(s).  Are you sure you calculated the derivative correctly?

babyslapmafro · Answer

What is f(x)?

anonymous · Answer

$$f(x)=(2x)/(x^2-1)$$

babyslapmafro · Answer

Yea you were right...

babyslapmafro · Answer

Well, the critical values of the function are x=+-i

babyslapmafro · Answer

Strange, but that is the answer....

anonymous · Answer

So is it possible to have no critical numbers?

babyslapmafro · Answer

Yes, a critical value occurs where the slope of the tangent-line is equal to 0.

babyslapmafro · Answer

Or I should say the critical value occurs where the value of the derivative is equal to 0.

babyslapmafro · Answer

And that can happen very often...

babyslapmafro · Answer

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babyslapmafro · Answer

that function does not have a critical value

babyslapmafro · Answer

i should say, on the interval shown, the function i drew does not have a critical value.

anonymous · Answer

and that would mean there are no inflection points?

babyslapmafro · Answer

Not necessarily, the function I drew, on the interval show, has no inflection points.  But you can have inflection points and not any critical values...

babyslapmafro · Answer

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