Consider the following table of values where t is hours after 12:00 p.m.
noon. A person left their home at 12:00 p.m. for a several hour road trip. The person
immediately got on the interstate. Let d(t) represent the distance in miles away
from the person is from their home and trepresent the number of hours since they
left.

The speed limit on the entire interstate is 65
miles per hour. According to the mean value theorem, during what interval of time was the
person definitely breaking the speed limit?

The piecewise function is shown in the
graph and from to has an average
rate of change of .

Find all values of c between
0 and 5 that satisfy the conclusion of the Mean-Value theorem.

a.

b.

c.

d.

The function is not continuous on the interval and
therefore isn’t guaranteed to have a value c that satisfies the conclusion of the
Mean-Value theorem.

e.

The function is
not differentiable on the interval and therefore isn’t guaranteed to
have a value c that satisfies the conclusion of the Mean-Value
theorem.

Farmer
Joe Bob Brown has 30 feet of fence and wishes to make a rectangular pen for his pig Wilbur with the
fence while using a barn as one of the sides of his pen. In square feet, what is the maximum
area for his pen?

A
cylinder is to be inscribed inside of a right cone with a radius of 5 cm and a height of 12 cm.
If the centers of the bases of the cone and the cylinder are the same, then determine the maximum
possible volume of an inscribed cylinder.