1). it is increasing at [-2,0]u[0,2] because the output is positive, above the x-axis. it is decreasing at (-∞,-2]u[2,∞) because the output is negative, below the x-axis.

2). there is a local minimum at x=0, and local maximum at x=-1.25, 1.25.

3). you cant tell with this graph because it is the graph of f '(x), it doesnt show the f(x).

4). the power function of f(x) is 5. it is 5 because the graph of the derivative has 4 slopes. by that i mean it changes the sign of the slope 4 times. so to get the derivative you subtract 1 off the power function and to find the f(x) you just add 1 to the f '(x).