Describe the graph

Question

Describe the graph of 

Answer 1

There are several things to look at when describing the graph. They are

1. x- intercept = -1, +3, +5
2. y- intercept = 3750
3. It has no vertical or horizontal asymptotes.
4. Critical points are x= -1, 5, 0.536, 3.46
5. Increasing on (-infinity, -1) U (0.536,3.46) U (3.46,5) U (5, +infinity)
6. Decreasing on (-1,0.536)
7. It has a local max at (-1,0)
8. Concave up at (-0.45,1.54) U (3.90,5) U (5,+infinity)
9. Concave down at (-infinity, -0.45) U (1.54, 3.90)
10. Inflection points are (-0.45,8.77), (1.54,8.59), (3.90,-8.95), (5,0)

Note: I might have done mistakes in these calculations but this is the concept to describe the graph. You obtain number 4 thru 10 by:

1. Determining the first and second derivative of the function
2. Calculating the critical points by setting the first derivative equation to zero.
3. Doing 1st derivative test with the factors and critical points you get to find the decreasing, increasing interval, and max and min.
4. the using second derivative test to find inflection points by setting up the second derivative equation to zero.
5. finally running the second derivative test to fin out the concavity of the graph.