MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A function is defined by f(x)=x3−3x for all real x.
(i) Explain, with reasons, why f(x) possesses both a local maximum and a local minimum although it has no absolute maximum or absolute minimum on R.
(ii) Describe how the positions of these local extrema can be located without evaluating the exact extreme values.
(iii) Comment on the behaviour of f(x) as x→∞ and as x→−∞, and relate this behaviour to the absence of absolute extrema.