LESSON 9 THE PRODUCT AND QUOTIENT RULES
Theorem (The Product Rule) If f and g are two differentiable functions and
k ( x ) = f ( x ) g ( x ) , then k ( x ) = f ( x ) g ( x ) + f ( x ) g ( x ) .
Proof By definition, k ( x ) = lim
h0
k( x + h ) k( x )
.
h
k
Exam 2 (3.43.9) M1850 10/23/2015
Name: 0 cfw_ (4" OIA
Read problems carefully and solve all given problems.
Show all your work clearly for possible partial credit.
Correct answer without a verification will receive a zero.
If you are not on the right tr
Quiz 8 (3,11 4,3)
M1850 11/05/2015
Name:
1. The diameter of a sphere is measured as 37 4 0.2 cm. Use the differential to estimate the error
in volume.
 /4
3
or 4o .ol
x2  5
2. Find at which point the following function has local extreme values: f(x) 
Quiz 9 (4.4 4.6)
M1850 11/12/2015 Name: .0 ( (A[
1. Find where the following function has local extreme points and inflection points:
1  1 4+ 7.
"n =  x3= o
f(x)
(a) local maximum at x = O
,/. (xi)=, '=o +"
(b) local minimum at x = :[
(c) inflection
M1850 11/19/2015 Name: ,i !. lT
Quiz 10 (5.1 5.3)
1. Use upper sum with three rectangles of equal width to estimate the area under the graph of
1
f(x) = and above the xaxis from x
x
= I to x = 3,
.=
, :z
? a
I 7 1 d3.4
3
a
.
q 3
= t_q: .,._ L :5 .z
Quiz 7 (3.10  3.10)
M1850 10/29/2015
Name: %cfw_u,zE,l/
1. A metal cube dissolves in acid such that an edge of the cube decreases by 0.6 ram/rain. How
fast is the volume of the cube changing when the edge is 5.4 mm?
=,#
dt
2. A spherical balloon is infla
Quiz 6 (3.6  3.6)
M1850 10/15/2015
Name:
1. Find the derivative of the following function: f(x) = X/ + 1. (Simplify your answer if
possible.)
2. Find the derivative of the following function: f(x) = esinz.
:= ot, .b =e , ?, e
3. Find the derivative of th
Quiz 5 (3.4  3.5)
M1850 10/08/2015
Name:
1. When a stone is thrown vertically upward from the surface of the moon at a velocity of 12.8
m/sec, it reaches a height of s = 12.8t  0.8t2 meters in t sec. Find how high the stone goes.

2.
Find the derivativ
Exam 1 (1.33.3) M1850 10/02/2015
Name:
Read problems carefully and solve all given problems.
Show all your work clearly for possible partial credit.
Correct answer without a verification will receive a zero.
If you are not on the right track, no partial
Quiz 3 (2.4 2.5)
M1850 9/17/2015
Name: i)/z'cfw_:i t
1. Find lira f(x) and lim f(x) and then find the limit lim f(x) if it exists for the following
x3
x3+
x3
l,x<3
function: f(x) = I,x + 2 , x > 3
.,y
2. Use lira
sin ax
sin x
 i, where a is a cons
LESSON 15 CONCAVITY AND THE SECOND DERIVATIVE TEST
Definition Let f be a function that is differentiable at c. Then
1.
the graph of f is concave upward at the point P ( c , f ( c ) ) if there exists an
open interval ( a , b ) containing c such that on the
LESSON 13 HIGHERORDER DERIVATIVES
The derivative of a function y = f ( x ) is itself a function. Can we differentiate the
function y = f ( x ) ? The answer is yes. The derivative of y = f ( x ) is called
the second derivative of the function f, and we wi
LESSON 2 FUNCTIONS
Definiton A function f from a set D to a set E is a correspondence that assigns to
each element x of D a unique element y of E .
x
.
.
y
f
D
E
Example Determine if the following is a function or not.
x
.
.
y
z
.
.
a
.
.
.
D
b
c
d
E
All
Quiz 1 (1.3  1.5)
M1850 9/03/2015
Name:
oI W.,
3
1. eosx = g and 7r < x < 27r. Find the following values:
sin x =
tanx =
_
#
3
2. Find all solutions of the following equation
vsinx + sin2x = 0,0 _< x < 2r
,s
/,=o,g, _g_,
r rr T(
2.
3. Sketch the grap