Consider the function f(x)=xlnx.

For the following questions, write inf for ∞, -inf for −∞, and None if no such answer exists.

a.) The domain of this function is .

b.) The x-intercept is .

c.) f′(x) = .

d.) f(x) is increasing on the interval and decreasing on .

e.) f(x) has a local minimum at and a local maximum at .

f.) f′′(x) = .

g.) f(x) is concave up on the interval and concave down on .

h.) f(x) has a point of inflection at .