# High School Math : Conceptualizing Derivatives

## Example Questions

### Example Question #1 : Derivatives

The speed of a car traveling on the highway is given by the following function of time:

Note that

What does this mean?

The car is not moving at time .

The car is not accelerating at time .

The car takes  seconds to reach its maximum speed.

The car is not decelerating at time .

The car's speed is constantly changing at time .

The car is not moving at time .

Explanation:

The function  gives you the car's speed at time . Therefore, the fact that  means that the car's speed is  at time . This is equivalent to saying that the car is not moving at time . We have to take the derivative of  to make claims about the acceleration.

### Example Question #1 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

The speed of a car traveling on the highway is given by the following function of time:

Consider a second function:

It represents the total distance the car has traveled at time .

It represents another way to write the car's speed.

It represents the change in distance over a given time .

It has no relation to the previous function.

It represents the rate at which the speed of the car is changing.