Question

I have the graph of a derivative of a fucntion (first derivative that is), how do i determince the where the max and min are, and where the intervals of increase and decrease are?

Answer 1

Draw a sign scheme for the derivative by setting it equal to zero. In the intervals in which the derivative is positive, the function is increasing, where it is negative, the function is decreasing. If the derivative changes sign at the point in which it is zero, it will either have a max or min here. In order to determine that, it will have a max if the sign goes from positive to negative, and a min if the sign goes from negative to positive.