Consider the function defined for all real numbers.
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the function g(x)=xe−x2 defined for all real numbers.
(1) Compute g′(x) and find all values of x at which g′(x)=0. (Show algebraic work.)
(2) Create a sign chart for g′(x) on the real number line and determine the intervals on which g is increasing and decreasing.
(3) Classify each critical point found in part (a) as a relative minimum or relative maximum and justify your conclusion.
(4) Rank the relative extrema from smallest to largest g-value. (Exact values or simplified expressions are acceptable.)