f(x) to f'(x)

1. increasing on (-2, 0)U(0, 2)
decreasing on (-∞, -2)U(2, ∞)

when you look at the graph of f'(x), the positive outputs are where f(x) is increasing.
this applies the same when looking at the negative outputs, where is f(x) is decreasing

2. if i were to round it,

local max at x=±1
local min at x=0

the local points are where the graph switches from a negative slope to a positive slope, or vice-versa

in this case, starting from the left, or negative side...

-the graph is going in a positive slope until x=-1, where is reaches its max and starts going down, or in a negative direction
-once it reaches x=0, the graph then starts going up, or in a positive direction

3. if i round, then..

concave up at (-∞, -1)U(0, 1)
concave down (-1,0)U(1, ∞)

where f'(x) outputs a negative slope, then that is where f"(x) is going to go down, or in a negative direction
-same thing when looking at the positive slope, but it will go in a positive direction

4. it has to be x to the fifth power because f'(x) shows that it's slope changes slope 4 times,

this means f'(x)=x^4, so

when finding the anti derivative, you add a power, so

f(x)= x^5