MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The derivative of a differentiable function is f′(x)=3x2−k, where k>0. State how many critical points f has, identify their x–coordinates, and indicate whether each is a relative maximum or relative minimum. Justify your identification using the sign of f′(x) on the intervals determined by the critical points.