**Problem1 :**Find the derivative of

*f*(

*x*) = 3

*x*

^{4}-2

*x*

^{2}+5

*x*

^{-1}and evaluate it at

*x*= 2 .

*f'*(

*x*) = 12

*x*

^{3}-4

*x*- 5

*x*

^{-2}and

*f'*(2) = 96 - 8 - 5/4 = 86 + 3/4

**Problem2 :**Find the velocity and acceleration functions corresponding to the position function

*x*(

*t*) = 3

*t*

^{2}- 8

*t*+ 458 .

*v*(

*t*) =

*x'*(

*t*) and

*a*(

*t*) =

*v'*(

*t*) =

*x''*(

*t*) , so using our basic calculus rules again we find that

*v*(

*t*) = 6

*t*- 8 and

*a*(

*t*) = 6

*t*

^{2}in

*x*(

*t*) .

**Problem 3:**What happens when a car which is traveling along at constant velocity screeches to a halt?

*deceleration*) of the vehicle (courtesy of good brakes). While the car was traveling at constant velocity, on the other hand, the acceleration was zero.