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

1. anonymous

@ganeshie8 @CGGURUMANJUNATH @Astrophysics

2. anonymous

@Owlcoffee

3. anonymous

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

4. anonymous

@Data_LG2

5. Owlcoffee

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

6. anonymous

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

7. Owlcoffee

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

8. anonymous

how i do that @Owlcoffee

9. Owlcoffee

Find the derivative first, what did you get?

10. anonymous

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

11. Owlcoffee

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

12. anonymous

how i do that @Owlcoffee

13. 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.