# High School Math : Introduction to 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 takes  seconds to reach its maximum speed.

The car's speed is constantly changing at time .

The car is not accelerating at time .

The car is not moving at time .

The car is not decelerating 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 : Derivative As A Function

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

Consider a second function:

It represents the change in distance over a given time .

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

It has no relation to the previous function.

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

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