Slope m

[nycmath]

Given the function f(x) = -3x + 7 we are told that the average rate of change of the linear function is the slope m of the linear function.

That is, [tex]\triangle y/ \triangle x[/tex] = -3.

We are also told that linear functions have a constant average rate of change.

Questions

1. Is the slope just another way to say the average rate of change?

2. Is the average rate of change in calculus called the derivative?

3. If so, can we say that the slope = average rate of change = the derivative in calculus?

[Eigenvalue]

1. Yes. The average rate of change is the slope.

2. A derivative is the instantaneous rate of change at a point.

3. It is somewhat true; the average rate of change is the slope, however, the derivative is the limit of the average rate of change as the interval approaches 0.

[nycmath]

1. Yes. The average rate of change is the slope.

2. A derivative is the instantaneous rate of change at a point.

3. It is somewhat true; the average rate of change is the slope, however, the derivative is the limit of the average rate of change as the interval approaches 0.

We will dive into the derivative later in Calculus 1.