F(x) from F'(x)

1. f(x) is increasing between [-2, about 1.3)U[0, about 1.3). I could tell this is the answer from the graph shown because wenever f'(x) has a positive output is where f(x) is positive.

2. local min at x= -2
local max at x= 2
Extrema can only occur when f'(x) is equal to 0 or is undefined, which is characterized by those two points. At x= -2 the sign changes from negative to positive therfore it being a local min. At x=2 the sign changes from positive to negative therefore being a local max.

3. The function f(x) is concave up at (-1,1) and convave down from (- infinity, -1)U(1, infinity). A function is concave up whenever f"(x)>0 and concave down when f"(x)<0. you can tell Weather its concave down when you see the graph of f'(x) is decreasing and concave up when the graph of f'(x) is increasing.

4.The graph of f'(x) would defenitly be a polynomial equation to the 4th power, now taking in consideration that the graph is the derivative of the origional graph f(x) must be a polynomial to the 5th power. p.s I looked at the notes ms.hwang gave us on how to tell how a polynomial equation would look if its higher than an equation to the 3rd power.