Homework Day 1
Due Thursday 3/31
Table One
A
B
0
3
2
3
4
3
6
3
Table Two
C
D
0
3
2
1
4
-1
6
-3
Table Three
E
F
0
1
0
2
4
3
4
4
Figure 1
1. Consider the relationships above in Table One, Two and Three (Figure 1). For each of the
given six (input, output)-r
1. The HW Graph represents 100 minutes of Eugenes bike trip.
Small HW Graph
Use large version for work
Download more than copy from hw page as needed
Calculus Concepts: Secant Line Average Rate of Change Tangent Line Derivative: D' (t )
a. Give two time i
y
1. The HW #1 graph is given on a separate sketch page.
7
6
5
4
3
2
1
x
-0.5
0.5
1
1.5
2
2.5
3
-1
a. The HW #1 graph is a function and its first and second derivatives. Label the curves
f ( x ) , f ' ( x ) and f ' ' ( x ) (you dont need to explain why fo
1.
Small HW #1 Graph
Use large version for work
Download more than copy from hw page as needed
a. Use the HW #1 graph page and carefully sketch tangent lines at x = 0 , x = 1 , x = 2 and
x = 3 for this function. Estimate the slope of each tangent line as
7. Willy Wonka wishes to make boxes of maximum volume to display their golden eggs. To
construct the boxes, the top and one end will be made of cellophane and the remaining
sides will be cut from a sheet of 24 inch 36 inch gold foil. They plan to cut out
3. Eugene has gone on an extended bike trip. Using the included graph and the list of data
points as you answer each of the following questions. Show all of your work for parts b)
and c).
As with Eugenes previous bike trips, t is time in minutes from the
Homework Day 3 (Due 4/7)
5. I need to fence in a new rectangular portion of my yard for my dog Mystic. I have
purchased 60 feet of fencing and I plan to use the house as one side of the pen.
a. Which configuration will give Mystic the most room? Support y
7. Willy Wonka wishes to make boxes of maximum volume to display their golden eggs. To
construct the boxes, the top and one end will be made of cellophane and the remaining
sides will be cut from a sheet of 24 inch 36 inch gold foil. They plan to cut out
1. The HW #1 graph is given on a separate sketch page. Which graph is the function and which
graph is the derivative? Label the curves f ( x ) and f ' ( x ) and carefully explain your choice
using key terms. Mark all key points on the graphs and/or axes.
1. Find the derivative of each of the following using the Product or Quotient Rules as
appropriate. Show your work. Dont simplify unless you are asked to.
a.
y = (1 + 3x)(1 + 5 x)
b.
1
y = 1 + 2 4 x 3 + 3 x 3 1 + 2 + 8 x 2
5x
c.
y = (1 + 3x)( x 3 + 5 x)
Final Homework Assignment Answers
Eugene, Rose and Corvy have discovered a secret portal to the planet Velocipede where the
gravitational constant is slightly less than the gravitational constant of earth. On Velocipede the
acceleration due to gravity is
MATH 495.595 / PRACTICE FINAL EXAM QUESTIONS
SOLUTIONS / COMMENTS
1. C is f ( x ) , A is f ' ( x ) and B is f ' ' ( x )
a
3a
a
a + + c = 99 c = 99
=b
2. a + b + c = 99
2
2
2
2
3
a
3a
99a
3a
9a 2
Maximize product a b c = a (99 ) =
= P(a )
P ' ( a ) = 99a
MATH 495.595 / PRACTICE MIDTERM EXAM QUESTIONS
Table One
A
B
0
2
1
3
2
3
3
4
Table Two
C
D
1
3
2
6
3
9
4
12
1. For each of the given (input, output) relationships in Tables One and Two; answer the
following: Is the relationship a function? Why or why not?
Topic 15 Homework (Due Tuesday 5/31)
1.
a.
b.
c.
d.
e.
2.
f ( x) = x 2 + 1
Using an interval of width 0.5, sketch f ( x) = x 2 + 1 from x = 2 to x = 3
with lower bound rectangles (to compute minimum areas) and sketch a second copy of
f ( x) = x 2 + 1 from
Topic 14 Homework (Due Tuesday 5/24)
1. Eugene and Rose have decided to sprint race again, this time for 20 seconds, their
speeds at 4 second intervals are recorded below. Both Eugene and Rose are
continually increasing their speed during the sprint.
Time