MA 22300
Take-home Quiz #9
Fall 2012
Name:
Section Number:
10-digit-PUID:
This is the only homework (counted as a quiz) that you need to do by hand and to turn in
for this course.
Due date: Friday, Nov. 2, 2012 (at the beginning of class)
1
MA 22300
Take-
QUIZ 8
MA223 011 and 021, Jose Lugo
October 19, 2012
Consider the function f (x) = 12x5 + 15x4 40x3 .
(7 pts) 1. Find the intervals of increase and decrease.
(3 pts) 2. Classify each critical point on the graph of f as a relative maximum, a
relative minim
LESSON 35
MA22300 0011 and 0021, Jose Lugo
November 12, 2012
Section 4.1. Exponential Functions
Exponential Functions. If b > 0 but b 6= 1, the exponential function with base b is
f (x) = bx .
x
y=
2x
x
1
y=
2
10
5
3
1 0
0.001 0.313 0.125 0.5 1
1024
32
8
Problem 60, page 213: The value V (in thousands of dollars) of an industrial machine is modeled
by
V (N ) =
3N + 430
N +1
2/3
where N is the number of hours the machine is used each day. Suppose further that usage varies
with time in such a way that
p
N (
LESSON 32
MA223 0011 and 0021, Jose Lugo
November 5, 2012
Section 3.5. Additional Applied Optimization
A FEW COMMON MISCONCEPTIONS
1. The Second Derivative Test (for relative extrema) does NOT talk about concavity! It
talks about certain critical points b
LESSON 19
MA223 011 and 021, Jose Lugo
October 3, 2012
Section 2.5. Approximations Using Increments
The greek (uppercase) letter (Delta) is used to denote change. So suppose we are
investigating the behavior of a function y = f (x), and are interested in
QUIZ 7
MA223 011 and 021, Jose Lugo
October 12, 2012
10, 780
units per month,
p
where p is the price p is the price per unit in dollars. It is projected that
t months from now, the price of the product will be p(t) = 0.4t3/2 + 3.8
dollars per unit. Find t
QUIZ 9
MA223 0011 and 0021, Jose Lugo
October 29, 2012
1
1
Consider the function f (x) = 1 + x4 x3 .
4
3
(6 pts) 1. Find all the critical points on the graph of f and apply the Second Derivative Test. What can you conclude?
(4 pts) 2. Use the first deriva
Lesson 23 (Answers)
2. The graph is rising for x < 3, so the derivative is positive on (, 3).
The graph is falling for x > 3, so the derivative is negative on (3, ).
4. The graph is falling for x < 1 and 3 < x < 5, so the derivative is negative on (, 1)
LESSON 41
MA22300 0011 and 0021, Jose Lugo
November 30, 2012
Section 4.3 Practicing some old stuff (continuation of section 4.3)
Example 1. Find an equation for the tangent line to y = f (x) at the specified point:
1. f (x) = xex ; where x = 0
2. y = 2x +
QUIZ 3
MA223 011 and 021, Jose Lugo
September 10, 2012
(6 pts) 1. Consider the function
(
2x + 1 if x 3
f (x) =
x2 1 if x < 3
Find:
(a) lim f (x)
x3
(b) lim+ f (x)
x3
(c) lim f (x)
x3
3x3 + 2x + 12
.
x+
5 2x3
If the limiting value is infinite, indicate wh
LESSON 22
MA223 011 and 021, Jose Lugo
October 12, 2012
Section 2.6. Related Rates Problems (continuation)
Example 1. (similar to #42) When the price of a certain commodity is p dollars per
unit, customers demand x hundred units of the commodity, where
x2
LESSON 38
MA22300 0011 and 0021, Jose Lugo
November 19, 2012
Section 4.3. Differentiation of Logarithmic and Exponential Functions
Derivative of the Exponential Function:
d x
(e ) = ex
dx
Example 1. Differentiate the given function:
1. y = ex + xe
2. f (x
LESSON 36
MA223 0011 and 0021, Jose Lugo
November 14, 2012
Section 4.1 Exponential Functions (continuation)
Compound Interest and Continuously Compounded Interest
Compound Interest. If P dollars are invested at an annual interest rate r (expressed as a
de
LESSON 42
MA223 0011 and 0021, Jose Lugo
December 3, 2012
Section 4.4 Additional Applications; Exponential Models
Exponential Growth and Decay
Exponential Growth and Decay. A quantity Q(t) grows exponentially if Q(t) = Q0 ekt
for k > 0, and decays exponen
LESSON 21
MA223 011 and 021, Jose Lugo
October 10, 2012
Section 2.6. Related Rates Problems
Example 1. (similar to #48) An environmental study for a certain community indicates
that there will be Q(p) = p2 + 3p + 1200 units of a harmful pollutant in the a
Quiz 1
MA223 011 and 021, Jose Lugo
August 24, 2012
Show all your work.
(4 pts) 1. Factor and simplify as much as possible:
10(x 5)2 (2x 1)2 20(x 5)(2x 1)3 .
(6 pts) 2. Simplify the quotient as much as possible:
3(x 2)4 (x + 5)7 6(x 2)5 (x + 5)6
.
(x 2)7
LESSON 34
MA223 0011 and 0021, Jose Lugo
November 9, 2012
Section 3.5. Additional Applied Optimization (continuation)
Example 1 (similar to #17, 18). A cable is to be run from a power plant on one side of
a river 900 meters wide to a factory on the other
QUIZ 4
MA223 011 and 021, Jose Lugo
September 12, 2012
Show all your work.
Consider the function f (x) = 2x2 3x.
(7 pts) 1. Find the derivative of f . Use the limit definition of the derivative.
You will not receive any credit if you give just the answer.