I need help on My Calc HW

Stuff like this is why people hate math. You've done your first derivative wrong - make sure you're doing the chain rule correctly.

 Spoiler

Use quotient rule.

[img]http://www.codecogs.com/eq.latex?f'(x) = \frac{(1)(x^2-x+1)^2-\frac{d}{dx}(x^2-x+1)^2(x-2)}{(x^2-x+1)^4}[/img]

Use chain rule.

[img]http://www.codecogs.com/eq.latex?f'(x) = \frac{(x^2-x+1)^2-2(x^2-x+1)(2x-1)(x-2)}{(x^2-x+1)^4}[/img]

Simplify.

[img]http://www.codecogs.com/eq.latex?f'(x) = \frac{(x^2-x+1)-2(2x-1)(x-2)}{(x^2-x+1)^3}[/img]

[img]http://www.codecogs.com/eq.latex?f'(x) = \frac{(x^2-x+1)-2(2x^2-5x+2)}{(x^2-x+1)^3}[/img]

[img]http://www.codecogs.com/eq.latex?f'(x) = \frac{-3(x^2-3x+1)}{(x^2-x+1)^3}[/img]

At the risk of bad algebra, this should be the first derivative.

Also, your Leibnitz notation is wrong. It's , not .

What are you asking for exactly? The answer itself? I'm not convinced you know what "inflection point", "concave up", and "concave down" even mean.