Curve sketching problem

f(x)=x²ln(x)

1. What is the domain of the function?
2. Does this function have any intercepts with the axis?
3. What are the turning points?
4. What is the x value of the point of inflection?
5. Sketch the graph.

Answers:

1. x>0
2. f(x)=0=x^2 ln(x)             x=1           f(x) has a x-intercept at (1,0).
3. f ‘(x)=2x ln(x)+x=0         x=0 & x=e^(-1/2)
4. f ”(x)=3+2ln(x)=0           x=e^(-3/2)
5.