Instantaneous Rate of Change

[nycmathguy]

Exercises 1.1
Question 10

I would describe the instantaneous rate of change of a car's position on a highway as a derivative of the derivative.

You say?

 

[MathLover1]

not quite as a derivative of the derivative , just derivative

The rate of change at one known instant or point of time is the Instantaneous rate of change. It is equivalent to the value of the derivative at that specific point of time. Therefore, we can say that, in a function, the slope m of the tangent will give the instantaneous rate of change at a specific
The change of position of an auto on the highway is called speed or velocity. Therefore, a change in that function would be called acceleration.
This limit is called the derivative of the Distance in function of time.
This is also why the derivative is called the instantaneous rate of change of a function.

 

[nycmathguy]

not quite as a derivative of the derivative , just derivative

The rate of change at one known instant or point of time is the Instantaneous rate of change. It is equivalent to the value of the derivative at that specific point of time. Therefore, we can say that, in a function, the slope m of the tangent will give the instantaneous rate of change at a specific
The change of position of an auto on the highway is called speed or velocity. Therefore, a change in that function would be called acceleration.
This limit is called the derivative of the Distance in function of time.
This is also why the derivative is called the instantaneous rate of change of a function.

Can you list the different names given to the limit in a calculus course? I would like to see that list. As you said "...the derivative is called the instantaneous rate of change of a function."

Any other names for the derivative?

 

[MathLover1]

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals
Derivative, in mathematics, the rate of change of a function with respect to a variable.

 

[nycmathguy]

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals
Derivative, in mathematics, the rate of change of a function with respect to a variable.

Thanks. Very cool. Math is cool.

 

[HallsofIvy]

I would have said that the cars "instantaneous rate of change of position" is given by its velocity.

 

[nycmathguy]

I would have said that the cars "instantaneous rate of change of position" is given by its velocity.

Understood. There's always a better way to make a statement.