The function f(x) from the graph f '(x)

1. Where is the function, f(x), increasing? Where is it decreasing? How can you tell from this graph? Explain.
   The function f(x) is increasing when the slope is greater than zero f '(x) > 0; therefore, at (-2, 0) U (0, 2). The function is decreasing when the slope is less than zero f '(x) <>; therefore, at (-∞, -2) U (2, ∞). The f '(x) graph, "outputs" the slope.
   
2. Where is there an extrema? Explain. (There are no endpoints.) There is a local minimum at (0,0), because at that point the slope changes from negative to positive.
   
3. Where is the function, f(x), concave up? Where is it concave down? How can you tell from this graph? The function has a positive concavity at (-∞, -1.25) U (0, 1.25) because that is where the slope of the graph of f '(x) is positive f ''(x) > 0. The function has a negative concavity at (-1.25, o) U (1.25, ∞) because it is where the slope of the graph is negative f ''(x) >0.
   
4. Sketch the graph f(x) on a sheet of paper. Which power function could it be? Explain your reasoning.