Find the points of inflection of the graph of the function.

f(x)= $\displaystyle x\sqrt{15-x}$

The second derivative

$\displaystyle f''(x)=\frac{45}{4\sqrt{x}}$

I can see that f''(x) is undefined at 0. There is no points of inflection.

Then why doesn't the upward concave exist but does the downward concave exist?

Can anyone help me explain it?