SOLUTION: Find the point of inflexion on the curve y=xln(x)-x^2. I found the derivative: y'= ln(x+1) -2x But I can't find the point of inflexion because I can't solve for y'=0 Please H

Question 1033076: Find the point of inflexion on the
curve y=xln(x)-x^2.
I found the derivative: y'= ln(x+1) -2x
But I can't find the point of inflexion because I can't solve for y'=0
Please Help !!!
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> y' = lnx + 1 - 2x ==> y" =
The critical values of the 2nd derivative are x = 0 and x = 1/2, but the function is undefined at x = 0, so there is no inflection point there.
Now in (, 0), y" < 0.
In (0, 1/2), y" > 0, and
at (1/2, ), y" < 0.
(At x = 1/2, y" = 0.)
Hence there is only one inflection point at (1/2, ). (Even though there is a change in the direction of concavity from the interval (, 0) to (0, 1/2).)

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