Given a function, find points, find limits, etc.

Given the function $\displaystyle f(x) = x^2ln(x)$, x is contained in the set (0,1)

A) Find the coordinates of any points where the graph of f has a horizontal tangent line.

B) Find the coordinates of any points of inflection on graph f

C) Find lim as $\displaystyle x --> 0^+ f(x)$ AND lim as $\displaystyle x --> 0^+ f'(x)$

D) Sketch graph of f using info obtained in a,b,c, with coordinates, max, min, etc.

The first 2 parts are based on units I did a WHILE ago ...

Do I do this for A?

$\displaystyle dy/dx = x + 2xln(x)$

$\displaystyle 0 = x + 2xln(x)$ (because 0 = horizontal line)

And solve for x?