intervals of increasing and decreasing, intervals of positive and negative, and extrema of F(x)=3/x^2-4+1

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intervals of increasing and decreasing, intervals of positive and negative, and extrema of F(x)=3/x^2-4+1

Mathematics
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just need this part @Owlcoffee intervals of positive and negative, and extrema of F(x)=3/x^2-4+1

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Well, you find the increase or decrease of any function, by derivating it. So, begin by derivating the function.
i did the increasing and decreasing i just need the positive and negitive and extrema @Owlcoffee
You still require to derivate the function and analyze the sign of it.
how i do that @Owlcoffee
Find the derivative first, what did you get?
-6x/(x^2-4)^2 @Owlcoffee
Okay, so now, you have to analyze the sign of each part, first the numerator and then the denominator. \[-6x=0\] \[x^2-4 \neq 0\]
how i do that @Owlcoffee
I'll give you the example usingthe numerator: \[-6x=0\] This is the numerator, and I can allow myself for it to be zero because it does not have problem with the existance, so I will only solve for "x": \[x=\frac{ 0 }{ -6 }\] \[x=0 \] Now, with the value of "x" that makes the numerator 0 I will draw a line that represent all the values of the "x" axis and what sign they image have: |dw:1436333122105:dw| So, this is what is called "studying the sign", which implies that I don't care what value the images of x gives, I am only interested in the sign, and by looking at the numerator, I know that when x tends towards inifnity the values will be negative and when it tends towards negative infinitiy they become positive.

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