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 x-wheel, a u-wheel, and a y-wheel. You can change the speed of the x-wheel, 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, 17-19, 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
* We aren't endorsed by this school
