Hey everyone, back again with another problem. So I have this:

(1/2)x^4 + x^3 - X^2 + 2

I need to find:

Critical Numbers

Critical Points

Relative Maxima and Minima

Concavity

Inflection Points

f'(x) = 2x^3 + 2x^2 - 2x. Taking out x I got (x)(2x^2 + 3x - 2)

The quadratic formula has given me the Critical Numbers: -2, 0, 1/2

Replaced them back in the original and after the 1DT got: (0, 2) = Rel. Max, (-2, 2) (1/2, 61/32(?)) = Rel. Min

Then f''(x) = 6x^2 + 6x - 2, and took out a two for 3x^2 + 3x - 1

Then for the quadratic formula I wound up with the concavity numbers of (-3 - square root 3)/6 and (-3 + square root 3)/6

Now I'm guess I did something wrong, since I don't think my professor would give me such messy numbers to work with. Otherwise I'd do the 2DT to get concavity and replace them in the original problem to get the inflection points... so I know what to do (I think) but I also think I'm messing up somewhere no matter how many times I retry it. Anyone know what's up?