Is this equation neither concave nor convex? This is so simple. I think I am just way over thinking it. It's about convex optimization.
When I solve it with the second derivative it's positive. When I plug it back in it's positive too. But then with the convex theorem (the whole $f(λx+(1−λ)y)≥λf(x)+(1−λ)f(y)$ stuff) does that mean it's concave because $713/243 > 2/4$? I am so confused.
It is neither convex nor concave.
The second derivative is $f''(x)=18x-4$, which is negative for $x \lt \frac29\approx 0.222$ and positive for $x \gt \frac29$
Part of it looks like