Name: 
 

03-01 - MVT, Critical Points, Optimizations



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

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 t represent the number of hours since they left.
mc001-1.jpg
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?
a.
between 12:00 p.m. and 12:30 p.m.
d.
between 4:12 p.m. and 5:00 p.m.
b.
between 12:30 p.m. and 1:30 p.m.
e.
between 5:00 p.m. and 5:36 p.m.
c.
between 1:30 p.m. and 2:00 p.m.
 

 2. 


The piecewise function mc002-1.jpg is shown in the graph and from mc002-2.jpg to  mc002-3.jpg has an average rate of change of mc002-4.jpg

Find all values of c between 0 and 5 that satisfy the conclusion of the Mean-Value theorem.
mc002-5.jpg
a.
mc002-6.jpg
b.
mc002-7.jpg
c.
mc002-8.jpg
d.
The function is not continuous on the interval mc002-9.jpg 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 mc002-10.jpg and therefore isn’t guaranteed to have a value c that satisfies the conclusion of the Mean-Value theorem.
 

 3. 

Locate the absolute extrema of the function  mc003-1.jpg on the closed interval mc003-2.jpg.



a.
mc003-3.jpg
d.
mc003-6.jpg
b.
mc003-4.jpg
e.
mc003-7.jpg
c.
mc003-5.jpg
f.
mc003-8.jpg
 

 4. 

The few values of the function mc004-1.jpg is shown in the table below.
mc004-2.jpg

mc004-3.jpg only has 2 critical points and is differentiable for all real values of  x.
Which of the number lines correctly describe where mc004-4.jpg increases and decreases?



a.

mc004-5.jpg
b.

mc004-6.jpg
c.

mc004-7.jpg
d.

mc004-8.jpg
e.

mc004-9.jpg
f.

mc004-10.jpg
 

 5. 


The function mc005-1.jpg is shown in the graph.



Given mc005-2.jpg is continuous for all real values of  x which of the number lines correctly describe where mc005-3.jpg increases and decreases?
mc005-4.jpg
a.

mc005-5.jpg
b.

mc005-6.jpg
c.

mc005-7.jpg
d.

mc005-8.jpg
e.

mc005-9.jpg
f.

mc005-10.jpg
 

 6. 

The graph of the function f(x) is shown at the right.


For which x-value is the function most likely to be continuous but NOT differentiable?
mc006-1.jpg
a.
mc006-2.jpg
d.
mc006-5.jpg
b.
mc006-3.jpg
e.
mc006-6.jpg
c.
mc006-4.jpg
 

 7. 

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?
mc007-1.jpg
a.
mc007-2.jpg
d.
mc007-5.jpg
b.
mc007-3.jpg
e.
mc007-6.jpg
c.
mc007-4.jpg
f.
mc007-7.jpg
 

 8. 

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.
mc008-1.jpg
a.
mc008-2.jpg
c.
mc008-4.jpg
b.
mc008-3.jpg
d.
mc008-5.jpg
 

 9. 

What is the approximate minimum distance from the point mc009-1.jpg to a point on the parabola mc009-2.jpg ?
mc009-3.jpg
a.
2.09
d.
2.93
b.
2.24
e.
3.12
c.
2.53
f.
3.67
 



 
Check Your Work     Start Over