MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the function h(x)=xe−x, x≥0.
(i) Find the intervals of increase and decrease of h(x) and identify all local extrema.
(ii) Determine the intervals of concavity and locate the points of inflection, if any, by using the second derivative.
(iii) Using the information from parts (i) and (ii), sketch a rough graph of h(x) on the interval [0,∞), clearly marking the critical points, points of inflection, and the behaviour as x→∞.