Question

Determine the concavity of
f(x)=xlnx

I end up with
F''(x)=1/x, where it would be concave up when x>0 and concave down when x<0
Is this correct?

Answer 1

y' = x(1/x) + lnx
= 1 + lnx
y'' = 1/x ---> yup, you had that

concave up when 1/x > 0 or x> 0
concave down when 1/x < 0, or x < 0

yes, you got it!