# Math Help - Concave upward and downward

1. ## Concave upward and downward

Find the points of inflection of the graph of the function.
f(x)= $x\sqrt{15-x}$

The second derivative

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

2. ## Re: Concave upward and downward

Originally Posted by dangbeau
Find the points of inflection of the graph of the function.
f(x)= $x\sqrt{15-x}$

The second derivative

$f''(x)=\frac{45}{4\sqrt{x}}$
I can see that f''(x) is undefined at 0. There is no points of inflection.
Where did you get that second derivative? Look at this.

3. ## Re: Concave upward and downward

Ah sorry, I also use that website but add inputs wrongly.
Then this one
$\frac{3(x-20)}{4(15-x)^{\frac{3}{2}}}$
There is no reflection points
while reading my book, I understand more about it (before that, I thought non-reflection points means non-concave upward and downward >.<)

So at x=15 f'' is undefined
Domain: $x\leq15$
Plug in 14 to f'' we get negative value=> concave downward

But I still don't understand why we have to test at the point f'' is undefined?