But when you take the derivative of both sides, you realize that the function f, which is graphed here, and if this were the x-axis, then this would be f of x. If this is the t-axis, then this is y is equal to f of t. But generally, this is the graph of our function f, which you could also view as the graph of g prime. If this is x, this would be g prime of x. 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.