And so we're thinking about the interval from, the open interval from five to 10, and we have g's derivative graphed here, and we wanna know a calculus-based justification from this graph that lets us know that g is concave up. So what does it mean to be concave up? Well, that means that your slope of tangent line, of tangent, tangent, slope of tangent is increasing, or another way of thinking about it, your derivative, derivative is increasing. Or another way to think about it, if your derivative is increasing over an interval, then you're concave up on that interval. And so we here, we have a graph of the derivative, and it is indeed increasing over that interval. So our calculus-based justification that we'd wanna use is that, look, f, which is g prime, is increasing on that interval. The derivative is increasing on that interval, which means that the original function is concave up.