Concavity and inflection points for f(x)=x-lnx

[bcahmel]

Homework Statement

determine the intervals on which the function is concave up or down and find the points of inflection.
f(x)= x-lnx for x>0

The Attempt at a Solution

f '(x)=1 -(1/x)
f"(x)= 1/x^2

I know to find concavity and inflection points you take the second derivative and set it equal to 0, then find intervals w/ the inflection point. But I don't know if I just took the derivative wrong but right now I can't solve the second derivative...any help, please?

 

[f!3ts]

Think about what the limiting values are for each of the terms as x goes to 0, infinity, 1, etc. Then try to sketch a plot of the curve, and plot it using a calculator to see how close you were. You'll be forced to think about how the function behaves and it might show you more than playing around with the algebra.

 

[bcahmel]

I get what you're saying, but I really need to know how to solve it with algebra...