$\displaystyle f(x) = 2x^2+2x+3$

Ok, so I know the function is increasing because $\displaystyle f^1(x)=4x+2$ which is positive

also it is concave up because $\displaystyle f^{11}=4$ which is also positive

Please teach me how to solve for local extreme points and inflection points, and for concavity, do I just answer concave up?