$f''(x) < 0$ and $f'(0) = 0$. Then, is the sum $f(0) + 2f(2) + 2f(4) + f(6)$ larger or smaller than $f$'s integral from $0$ to $6$?
Does the answer change when we have $f(x) > 0$ for $x \geq 0$?
Attempt
I thinks the answer should be "cannot be determined with the available info", even with the extra condition. Because the sum could be smaller than the lower Riemann on the partition with points $0,2,4,6$, or it could be less than the upper Riemann sum on the same partition.