# Find the points on inflection and discuss the concavity of the graph of the function?

• Sep 16th 2007, 02:20 PM
liz155
Find the points on inflection and discuss the concavity of the graph of the function?
I need to find the points on inflection and discuss the concavity of the graph of the function:

f(x)= (x+1)/(sqrt(x))

I know that points of inflection require setting the second derivative equal to zero and finding where it is undefined.

Here is my work so far...
f(x)=(x^(-1/2))(x+1)
f(x)=x^(1/2)+x^(-1/2)
f'(x)=1/2x^(-1/2) -1/2x^(-3/2)
f''(x)= -1/4x^(-3/2) +3/4x^(-5/2)

My problem is that when I find the zeros of f''(x) I get x=3. That makes sense. But when I see where it is undefined, it is undefined from (-infinity,0).

How can I use this information to find points of inflection and where the graph is concave up/down?

Thanks so much!!! :):):)
• Sep 16th 2007, 02:53 PM
TKHunny
Forget the derivative for a moment. What is the Domain of f(x)?

Are you really surprised that the second derivative doesn't exist for x <= 0?

You can check the sign of the first derivative on both sides of the point of inflection to see the concavity.