F is concave up on the interval. Well, just because your derivative is concave up doesn't mean that your original function is concave up. In fact, you could have a situation like this where you're concave up over that interval, but for much of that interval right over here, if this was our graph of f or g prime, we are decreasing, and if we're decreasing over much of that interval, then actually on this part, our original function would be concave down. The graph of g has a cup u shape on the interval. Well, if we had the graph of g, this would be a justification, but it wouldn't be a calculus-based justification. Let's do more of these. So this next one says, so we have the exact same setup, which actually all of these examples will have, g of x is equal to this thing here.