Sketch the graph of the function, using the curve-sketching guide.(adsbygoogle = window.adsbygoogle || []).push({});

Function: [tex] \frac {x}{x^2-4} [/tex]

So far I have derived this information from the function:(Please check!)

Domain: [tex] (-\infty,-2)\cup(-2,2)\cup(2,\infty) [/tex]

y-int: (0,0)

x-int: (0,0)

Asymptote: x=-2 , x=2

First Derivative: [tex] f'(x)=\frac {-x^2-4}{(x^2-4)^2} [/tex]

Second Derivative: [tex] f''(x)=\frac {2x(x^2+12)}{(x^2-4)^3} [/tex]

The information that I need now is where it is increasing and decreasing; the relative minimum; where it concaves up and down; and the points of inflection. My problem is, when I plug in zero for y in the derivatives, it gets complicated. For example, the first derivative:(Please check!)

[tex] \frac {-x^2-4}{(x^2-4)^2}=0 [/tex]

[tex] -x^2-4=0 [/tex]

[tex] -x^2=4 [/tex]

[tex] x^2=-4 [/tex]

[tex] x=\sqrt{-4} [/tex]

Correct me if I'm wrong, if you square root a negative number, wouldn't you have to use imaginary numbers [tex] (\imath) [/tex]? Any help will be greatly appreciated!

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# Homework Help: Need help on graphing this function.

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