Function f(x) from the graph f'(x)

1. The function is increasing from (-2,0)U(0,2) because between these intervals you get positive outputs. The function is decreasing from (-∞,-2)U(2,∞) because all the outputs in these intervals give you a negative output.


2. I think there are three extrema because at three points the slope is equal to zero. At f'(o) the slope is equal to zero which means it is a critical point. Two other points where the slope is equal to zero is at f'(-2) and at f'(2) which makes them two other critical points.


3. The function is concave up at about (-∞,-1.2)U(0,1.2) because between theses intervals f''(x) is greater than zero. The function is concave down at (-1.75,0)U(∞,1.75) because f''(x) is less than zero.


4. The power function could be -x^5 becuase the f'(x) is negative so i'm guessing would be negative as well. And f'(x) curves four times so the power funtion would be one more up.