### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem 6-75

6-75.

While riding his bike to a pond, Steven's distance in miles was modeled by

*s*(*t*) below. If the lake was 9 miles away and if*t*is measured in hours: Homework Help ✎

*s*(*t*) =*t*^{3}− 3*t*^{2}+ 3*t*What was Steven's maximum velocity during the trip? When did it occur?

Did Steven ever stop during the trip? Justify your conclusion analytically.

What was Steven's average velocity?

*v*(*t*) = 3*t*^{2} − 6*t* + 3 = 3(*t* − 1)^{2}

Visualize *v*(*t*). It is a concave up parabola; therefore there cannot be a local maximum. But Steven didn't ride his bicycle forever! You can still find the maximum velocity during the time interval when Steven was on his bike... Check the Endpoints!

Does *v*(*t*) ever equal 0 during the time interval of Steven's bike ride?