f(x) from f'(x)

Woohoo... MORE graphs... (Yes, people, that was sarcasm). Okay, ANYWAYS...

1. f(x) increasing on interval [-2, 2] because f'(x)>0
f(x) decreasing on interval (-∞, -2]U[2, ∞) because f'(x)<0
2. Extrema are at x=-2--> minimum, because f'(x) changes from negative to positive and at x=2--> maximum, because f'(x) changes from positive to negative.
3. For the sake of simplicity I'll round to the nearest whole number...
Concave up on interval (-∞, -1]U[0, 1] because f"(x), aka the slope of f'(x), is positive
Concave down on interval [-1, 0]U[1, ∞) becasue f"(x) is negative
4. I want to say that f(x) might be somthing like -x^5
since it looks somewhat like -x^3 with a bunch of crazy stuff happening in the middle...