AP Calculus Slides December 7, 2007

The document discusses a family of polynomial functions f(x) = ax^3 + bx^2 + cx + d where a, b, c, and d are constants. It asks the reader to: 1) Identify the x-values where f may have relative extrema points based on the first derivative. 2) Set up an equation using the Mean Value Theorem to find an x-value in the interval [-1,1]. 3) Note that if a>0, the function f would be concave up based on the second derivative test. The document also provides numbers that satisfy the Mean Value Theorem for two given intervals as examples to review for an upcoming test.