MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=x3−6x2+9x+15 be a polynomial defined for all real x.
(i) Find all critical points of f(x).
(ii) Classify each critical point as a local maximum, local minimum, or neither.
(iii) Determine the open intervals on which f(x) is increasing and those on which it is decreasing.