Let be defined on the half-open interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

h(x)=x\ln x

be defined on the half-open interval

(0,4]

. (i) Evaluate

\displaystyle \lim_{x\to 0^{+}} x\ln x

. (ii) Find all critical points of

h

(0,4]

. (iii) Using the information from parts (i) and (ii), determine the absolute minimum and absolute maximum values of

h

(0,4]

, specifying the points (or limit point) where they occur.