Let $$f(x) = x\!\left(x-3\sqrt{x}\right)$$ Determine the intervals on which the given function is concave up or down and find the point of inflection. (Help with interval notation.)

The x-coordinate of the point of inflection is

In the next two questions give the largest interval in the domain of $f$ that fits the description.

The interval on the left of the inflection point is . On this interval $f$ is ?? Concave Up Concave Down .
The interval on the right of the inflection point is . On this interval $f$ is ?? Concave Up Concave Down .