Unit Five (Part 1) Ap Calculus Take-Home Packet 5 Optimization Math Worksheet Page 2
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8Unit Five (Part 1)
AP Calculus Take-Home Packet
Optimization
JOKING AROUND WITH OPTIMIZATION PROBLEMS
Directions: Solve each of the problems below. Find the correct answer in the column at the right. Then
place the corresponding word in the appropriate blank to answer the two corny questions at the bottom of
the page.
1. Determine the constant a in order that the
2, 0
AT
a
2
function
will have a point of
y
x
4, 0
BE
x
9
x
COMPOSING
1.
inflection at
12
DECOMPOSING
2. Determine the volume of the largest right
54
EXTRA
circular cylinder that can be inscribed in a given
circular cone with radius 3 and height 9.
3. Determine the minimum point(s) of
FORTUNE TELLER
2
2 .
y
x
1, 0
LARGE
3
1
4. Where does the graph of
have a
y
x
MEDIUM
16
point of inflection?
4
2
2
4
5. Sketch the graph of
.
y
x
x
MIDGET
6. Sketch a smooth curve
y
f x
SMALL
3
4,
0 for
3,
illustrating
f
f
x
x
f
3
0,
0 for
3.
f
x
x
HE
7. Determine the constant k in order that the
k
2
function
will have a relative
f x
x
x
STILL
x
2.
minimum at
1
IS
Question #1: What were the headlines after a midget fortuneteller escaped from jail?
________________
________________
________________
____________
#6
#7
#3
#4
Question #2: Why does Beethoven spend all his time erasing music?
_______________________
____________________
__________________
#5
#1
#2
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