Although differentiation helps you figure out a lot of things about a function, there's one thing that differentiation cannot answer: What's the function's average height? To answer that, you need integration.

The following practice questions ask you to find average values using integration.

## Practice questions

What's the average value of

A car's speed in feet per second is given by

*f*(*t*) =*t*^{1.7}– 6*t*+ 80. What's its average speed from*t*= 5 seconds to*t*= 15 seconds? What's that in miles per hour?

## Answers and explanations

The average value is 0.03.

Do this with a

*u*-substitution.The car's average speed is about 72.62 feet per second, or 49.51 miles per hour.