CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
1. If the marginal cost is constant, then it equals the average cost. True
False
2. The derivative of a product is the product of the derivatives. True
False
3. The derivative of a difference is the difference of the derivatives. True
False
4. The derivat
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
1. f(x) = x is differentiable at every point of its domain. True
False
2. If y = f(x), then f (x) =
dy
dx
. True
False
3.
dy
dt
is dy divided by dt. True
False
4. If y = f(x), then f (x) measures the instantaneous rate of change, whereas
dy
dx
measures
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
1. If f(x) is not defined, then
lim
xa
f(x) does not exist. True
2.
lim
x1
False
x
x1
does not exist. True
False
3. If f is continuous at x = a, then
lim
xa
f(x) = f(a) True
False
4. If f(x) does not approach 3 as x 4 then f(4) 3. True
5.
lim
x
2
x2 4
x2
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
Applied calculus True false quiz: Functions and linear models
1. A mathematical model can never be a linear function. True
False
2. Every straight line is the graph of a linear function of one variable. True
False
3. The graph of every linear function of
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
The Intuitive Notion of the Chain Rule
In the applet we see an xwheel, a uwheel, and a ywheel. You can change the speed of the xwheel, and you can
connect the wheels with belts and change their radii. We'll use this model to explore the chain rule and
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
r
+)
Let's examine the slopes of secant Jines beginning with the point (2,
and fixed point (6,3). We will choose points closer and closer
to P (6,3) by choosing x  values closer and closer to 6 but less than 6. Fill in the table below.
Point
Fixed Point
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
/
Math 6'4
The Tangent Line Problem
What does it mean to say that a line is tangent to a curve at a point? For a circle, the tangent line at a point P is the line that is
perpendicular to the radical line at point P, as shown in the figure below.
y
Tangen
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
Section 3.1 Powers and Polynomials
HW: 17, 21, 23, 29, 31, 33, 35, 37, 43, 45, 47, 55, 65
Derivatives of a Constant Multiple
If f is differentiable and c is a constant, then d cf x
dx
Derivative of Sum and Difference
If f and g are differntiable, then d f
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
Math 614
Section 2.4  Read
HW: 1, 3, 5, 13, 19
Section 2.5 The Second Derivative
HW: 3, 5, 9, 11, 15, 17, 21, 29, 31
Since the derivative is itself a function, we can consider its derivative. For a function f, the derivative of its
derivative is called t
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
2.1 How Do We Measure Speed?
HW: 9, 1719, 21
The speed of an object at an instant in time is surprisingly difficult to define precisely. There is some paradox in
trying to study motion at a particular instant in time, since by focusing on a single instan
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
1.6 Powers, Polynomials, and Rational Functions (HW: 11, 13, 21, 23,
Power Functions
Definition: A power function has the form fx kx p , where k and p are constant.
Odd powers of x are Seat shaped for p 1 (Figure 1) and even powers of x are shaped (Figure
CALCUL US F OR TEACHERS I CLASS NO. 2131 (3.0 semester hour
MATH 614

Spring 2014
Math 614
Review from Section 1.2:
While a linear function can be used to model population growth that has a constant increase or decrease in the
number of people, an exponential function can be used to model population growth that has a constant percentag