### All High School Math Resources

## Example Questions

### Example Question #1 : Conceptualizing Derivatives

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

Note that

What does this mean?

**Possible Answers:**

The car takes seconds to reach its maximum speed.

The car is not accelerating at time .

The car is not moving at time .

The car's speed is constantly changing at time .

The car is not decelerating at time .

**Correct answer:**

The car is not moving at time .

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 #2 : 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:

What can we conclude about this second function?

**Possible Answers:**

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

It has no relation to the previous function.

It represents the change in distance over a given time .

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

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

**Correct answer:**

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

Notice that the function is simply the derivative of with respect to time. To see this, simply use the power rule on each of the two terms.

Therefore, is the rate at which the car's speed changes, a quantity called acceleration.

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