MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f be the polynomial function defined by f(x)=x3−3x2−9x+5. The domain is all real numbers.
(1) Determine all critical points of f. Show analytical work leading to their x-coordinates.
(2) Classify each critical point found in part (a) as a local maximum, a local minimum, or neither. Support your answer using an appropriate derivative test.
(3) On the closed interval [−2,5], evaluate f at the critical points and at the endpoints to decide the absolute (global) maximum and minimum values of f. Present your final answers in ordered pairs (x,f(x)). Clearly connect the values you compute to your conclusion.