the change in the function Δf

函数的变化量 Δf
is the derivative of the function at the starting point

等于函数在起点处的导数
times the distance you move.

乘以移动的距离
This is not an equality,

这不是一个精确等式
unless f happens to be a straight line;

除非 f 恰好是直线
it's an approximation and there are corrections to this.

这只是个近似的关系并且有修正量
That's what all the dots mean;

这就是这些点的意思
corrections are proportional to Δx^2 and Δx^3 and so on.

修正量与 Δx^2 和 Δx^3 之类的项成比例
But if Δx is tiny,this will do; that's it.

但如果 Δx 很小这个就足够了就这样
But today, we are going to move

今天我们要把
the whole Work Energy Theorem and

整个功能原理和
the Law of Conservation of Energy

能量守恒定律