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

1.The function is increasing from negative infinity to -1, and 0 to 1
the function is decreasing from 1 to 0, and 1 to infinity. The slope determines when the function is increasing or decreasing, and the given graph is the slope of the original function.

2. There is a local max at (1,4), because that is the point where the slope of the function changes from positive to negative.

3.The Function is concave up from x=0 to x=1, because that is where the slope of the given graph is positive, and the function is concave down at x=1 to infinity because that is where the slope of the given graph is negative.

4. The given graph is x^4 and that graph is the derivative of the original function which is not given. If you were to take the antiderivative, it could be x^5 or x^5+c