1. The problem statement, all variables and given/known data Please state the following components of this rational function? f(x)=6x^2/(x^2-2x-15) -intervals of increase/decrease -local maximum and minimum values -intervals of concave up/concave down -points of inflection 2. Relevant equations N/A 3. The attempt at a solution There is a horizontal asymptote at y=6. There are vertical asymptotes at x=-3 and x=5 The first derivative is -12x(x+15)/(x^2-2x-15)^2 The second derivative is 12(2x^3+45x^2+225)/(x^2-2x-15)^3 According to the first derivative, the critical numbers would be -15, and 0. After the first derivative test, I found out that a min. point occurs when x=-15 and a max. point occurs when x=0. However, I got (-15,5.625) and (0,0). How can the min. point have a larger y-value than the max. point? Also, when I graphed this function on GraphCalc, it seems that there does not seem to be a minimum point at x=-15. Why is that? When I graphed the function, there seems to be 3 branches; in the left, middle, and right. The left branch seems to go through the horizontal asymptote (y=6) but then it slowly approaches it from below y=6. Please graph f(x)=6x^2/(x^2-2x-15) at http://math.ucalgary.ca/undergraduate/webwork/graphing-calculator [Broken] to see what I am describing. I cannot justify why there would be a minimum at x=-15.