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

Question

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

saylilbaby · Answer

@ganeshie8 @CGGURUMANJUNATH @Astrophysics

saylilbaby · Answer

@Owlcoffee

saylilbaby · Answer

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

saylilbaby · Answer

@Data_LG2

owlcoffee · Answer

Well, you find the increase or decrease of any function, by derivating it.
So, begin by derivating the function.

saylilbaby · Answer

i did the increasing and decreasing i just need the positive and negitive and extrema @Owlcoffee

owlcoffee · Answer

You still require to derivate the function and analyze the sign of it.

saylilbaby · Answer

how i do that @Owlcoffee

owlcoffee · Answer

Find the derivative first, what did you get?

saylilbaby · Answer

-6x/(x^2-4)^2 @Owlcoffee

owlcoffee · Answer

Okay, so now, you have to analyze the sign of each part, first the numerator and then the denominator.
$$-6x=0$$
$$x^2-4 \neq 0$$

saylilbaby · Answer

how i do that @Owlcoffee

owlcoffee · Answer

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.