Homework Help: Derivatives & the Slope of a graph

1. The problem statement, all variables and given/known data
Given




2. Relevant equations


3. The attempt at a solution

 

I know I found that it is increasing on the interval (-1,1), but that's wrong

 

ok I re-did it again because I found an error
now I got (-1,3) for increasing
and (-infinity, -1) U (3, infinity) for decreasing
and I got it by doing the number line test (i think that's what it's called)
where I take all the criticals numbers and line them up and put test numbers in between them.

 

it's a straight light, and on the original function that means that there's a point there where it is neither increasing or decreasing or a max or min.
I found an answer for them, but I'm not really confident
f(3)= error.....
f(-1)= 9/16
I'm suppose to get two numbers but I think I did something wrong again....I hate these problems....

 

in the numerator: -1,1
denominator: 1/3, 3
dang it I redid it again and this time I got (-1,1) as increasing and I know that's wrong....

 

That's what I did when I first started it and I got (-1,1) as increasing but that's wrong.....

 

there's an error at 3 too, so does that mean I do count the denominator?
Even if I do count the denominator I get an error as the maximum

 

huh?
oh are you saying because it's undefined there its (-1, 1/3) U (1/3, 1)???

 

ok, so I redid it over again and do you think these are correct:

b) (-1, 1/3) U (1/3, 1) --increasin interval
c) (-infinity, -1) U (1, 3) U (3, infinity) --decreasng interval
d) f(1)= 1/4 --max
e) f(-1)= 9/16 ---min

 

nothing important, that was a typo, how about this for an answer:
(-infinity, -1) U (1, 3) U (3, infinity) --decreasng interval

 

Thanks guys the answers were right :)