So the velocity at any part of the curve is tangent to the curve at that point.

曲线上任意一点的速度,都在该点和曲线相切

耶鲁公开课 - 基础物理课程节选

The exact shape of the curve is subject to discussion, but the point of diminishing marginal utility is that, as you get more and more money, the increment in utility for each extra dollar diminishes.

这条曲线的确切形状还有待讨论,但是边际效用递减规律的重点在于,你得到的钱越多,每额外的一美元的增长效用会相对减小

耶鲁公开课 - 金融市场课程节选

At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.

在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度

耶鲁公开课 - 基础物理课程节选