MA 220 Exam 2 Answers, Spring 2012
Problem
1)
2)
Form A
A
Form B
C
Actual Answer
5
A
B
x 5, 0, 2, 3, and 6 only
(Problem 2 will be a free problem, however. All answers will be counted.)
3)
B
E
15 x 2
4)
B
D
m 48
5)
A
A
5
6)
B
E
y 3x 6
7)
B
D
$13.80
8)
D
E
MA 22000 Notes, Lesson 36, (2nd half of text) section 4.2
Natural Exponential Functions
Summary: A general and basic exponential function is f ( x) a x , where the base, a is any
positive number except one.
Examine the function values for various bases.
A
MA 22000 Lesson 42 Notes Section 4.6, Exponential Growth and Decay Quote from textbook (page 299): "Real-life situations that involve exponential growth and decay deal with a substance or population whose rate of change at any time t is proportional to th
MA 22000 Lesson 41 Notes Section 4.5 (2nd half of text) (Continuation of derivatives of logarithmic functions) Reminder of rules of derivatives of logarithmic functions: Derivative of the natural logarithmic function:
d 1 [ln x] dx x
(In words, the deriva
MA 22000 Lesson 40 Notes Section 4.5 (part 1) Derivative of the natural logarithmic function:
d 1 [ln x] dx x argument.)
(In words, the derivative of a natural logarithmic function is the reciprocal of the
Let u be a function of x, then d 1 1 du [ln u ] u
MA 22000 Lesson 39 Lesson Notes
(2 half of text) Section 4.4, Logarithmic Functions
nd
Definition of General Logarithmic Function:
A logarithmic function, denoted by y logb x , is equivalent to b y x .
In previous algebra classes, you may have often used
MA 22000 Lesson 37 Notes Section 4.3 (part 1), Pages 273 280 Derivative of the NATURAL EXPONENTIAL Function
d x dy [e ] e x or if y f ( x) e x , y ex dx dx d u dy du du [e ] eu or if y f (u ) eu , euu or eu cx dx dx dx (using chain rule)
Example 1: Find t
MA 22000 Lesson 33 Notes 3 part of section 3.4 and section 3.5
rd
We will continue to use the same guidelines for finding maximum or minimum values as in the previous two lessons. Example 1: A rectangular page is to contain 64 square inches of print. The
MA 22000 Lesson 32 Notes Review of Guidelines for Optimization Problems (finding maximums or minimums). An optimization problems involves finding a value that would determine a maximum or minimum for a problem. For many of these problems, you will have to
MA 22000 Lesson 31 Notes Section 3.4 Optimization Problems An optimization problems involves finding a value that would determine a maximum or minimum for a problem. For many of these problems, you will have to write two equations initially. The primary e
MA 220 Lesson 30, Section 3.7 (part 2)
Curve Sketching:
1)
Find (if possible) any y-intercept or x-intercepts. To find y-intercept, let x = 0 and
solve. To find x-intercept(s), let y = 0 and solve. (Finding x-intercept(s) is not always be
easy to accompli
MA 220 Lesson 29, Section 3.7 (part 1) Curve Sketching: 1) Find (if possible) any y-intercept or x-intercepts. To find y-intercept, let x = 0 and solve. To find x-intercept(s), let y = 0 and solve. (Finding x-intercept(s) is not always be easy to accompli
MA 220 Lesson 28 Notes Section 3.3 (p. 191, 2nd half of text) The property of the graph of a function `curving' upward or downward is defined as the concavity of the graph of a function. Concavity if how the derivative (that describes if a function is dec
MA 22000 Lesson 27 Notes (2nd half of text, section 3.2) Relative Extrema, Absolute Extrema in an interval In the last lesson, we found intervals hwere a function was increasing or intervals where that function was decreasing. At a point, where a function
MA 22000, Lesson 26 Notes Section 3.1 A function is increasing if its function values (y's) are rising as x values get larger. A function is decreasing if its function values (y's) are falling as x values get larger. Formal Definition: A function f is inc
Even Answers: Chapter 1 (2nd half of textbook)
Section 1.3
36)
y 2 x 2 or 2 x y 2 0
38)
y x 3 or x y 3 0
40)
y 1 or y 1 0
42)
x2
46)
y
16
79
x
or 16 x 15x 79 0
15
15
54)
y 2 x 6 or 2 x y 6 0
80)
a)
86)
V 30000t 825000, 0 t 25
88)
3014 students
90)
a)
c)
S
Even Answers for Chapter 2 Problems (2nd half of text) Section 2.1 6) 50) 54) slope is
4 3
8)
slope is
1 4
10)
slope is -3
differentiable at all x except -3 and 3, where there are cusps (, 3) (3,3) (3, ) differentiable at all x except -2 and 2, where the
MA 22000
Final Exam Practice Problems
1. If f (x) = -x2 - 3x + 4, calculate f (-2). A. -6 B. 0 C. 2 D. 6 E. 14 2. If f (x) = 2x2 - x + 1, find and simplify f (x + 2). A. 2x2 - x + 3 B. 2x2 + 7x + 7 C. 2x2 - x + 7 D. 2x2 + 7x + 11 E. 2x2 - x + 11 3. Simpli
MA 22000 Lesson 38 Notes Section 4.3 (2nd half of text) part 2 This is a continuation of finding derivatives of exponential functions. Example 1: Find each derivative.
a ) f ( x ) x (e )
2 2x
b)
2e x x2
c)
e x e x g ( x) 4
d ) F ( x) x3e x e x
e)
f ( x) 2