Bc Fiesta6
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AP CALCULUS BC | 2008 | Shubleka | Fiesta # 6
Name________________________
Please write your answers neatly on a separate sheet. Show and justify your work for full credit. No calculators are allowed. Problem 1: a) Show that a cubic function (a third degree polynomial) has exactly one point of inflection. b) If the graph of a cubic function has three x-intercepts, show that x-coordinate of the inflection point is equal to the average of the three zeros. Problem 2 Use calculus to discuss: f ( x) =
x3 x 2 +1
g ( x) =
2 x2 x 2 −1
.
Name________________________
Please write your answers neatly on a separate sheet. Show and justify your work for full credit. No calculators are allowed. Problem 1: a) Show that a cubic function (a third degree polynomial) has exactly one point of inflection. b) If the graph of a cubic function has three x-intercepts, show that x-coordinate of the inflection point is equal to the average of the three zeros. Problem 2 Use calculus to discuss: f ( x) =
x3 x 2 +1
g ( x) =
2 x2 x 2 −1
.
