The average change rate is the ratio of the increment of y to the increment of x, which can be used to observe the change speed of the function and how the function changes. You can also learn the average rate of change before learning the derivative, which will pave the way for later learning the derivative.

Application:

Observe the changing speed of the stock.

We can use the knowledge of average change rate to find out the average change rate of a stock in a certain period of time, so as to understand the trend and future trend of this stock.

Pave the way for learning derivatives

Derivative is a very important knowledge point in calculus. The derivative can be understood as when ▲x approaches 0.

, the limit of the average rate of change, namely lim ▲ y/▲ x.

. You see, the derivative is actually the limit of the average rate of change when the increment tends to zero. Can we learn the derivative better by learning the average rate of change first?