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?

f(x) is increasing from (-2,0)U(0,2). because f(x) is increasing when f '(x) > 0.

f(x) is decreasing from (-∞,-2)U(2,∞). because f(x) is decreasing when f '(x)<0.

2. Where is there an extrema? Explain. (There are no endpoints.)

extrema is at (0,0). because an extrema can only be found at a critical point, and a critical point is where f '(x)= undefined or 0. as we can see... f '(0)=0

3. Where is the function, f(x), concave up? Where is it concave down? How can you tell from this graph?

it concaves up where the slope of f '(x) is positive and concaves down where the slope of f '(x) is negative.

concaves up: (-∞,-1.25)U(1.25,∞)

concaves down: (-1.25,0)U(1.25,2)

4. Sketch the graph f(x) on a sheet of paper. Which power function could it be? Explain your reasoning.

looks like an x^5. because it changed directions 4 times. also, f '(x) looks like an x^4 function. so briefly, the antiderivative of x^4 is somewhere around x^5 something... so i am assuming that f(x) is 5th power function.