X intercepts of Logrithms using Derivatives

[Dysney]

Consider f(x) = x ln(4 – x2), for –2 <x< 2

LetP and Q be points on the curve of f where the tangent to the graph off is parallel to the x-axis.
(i) Find the x-coordinate of P and ofQ.

I've been working on this problem for over an hour (the image includes the graph, hope you guys can see it okay)

And I've been trying to find the x intercepts of this function, and have been trying to find the derivative and set it to zero, but none of the answers I found matched the answer key. Help please? I'm not even sure if I'm on the right track

 

[Ishuda]

I've been working on this problem for over an hour (the image includes the graph, hope you guys can see it okay)

And I've been trying to find the x intercepts of this function, and have been trying to find the derivative and set it to zero, but none of the answers I found matched the answer key. Help please? I'm not even sure if I'm on the right track

What did you get for the derivative of
f(x) = x ln(4 – x²), for –2 <x< 2?

Can you see that either x=0 or 4–x²=1 if f(x) is to be zero? In the latter case, what does that mean x must be?

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

EDIT: BTW, notice that f(-x)=-f(x) so that you really have to find P. Q is then minus P.