MA 1170 Homework 15 Answers
For each of the given functions, nd the critical points, and use the second derivative test. Your answers
should be relative max, relative min, or dont know.
1.
f(x) = x2 3.
f (x) = 2x, so x = 0 is the only critical point. The
MA 1170 Practice Test II
Name
1.
Use the product rule on the following. Dont simplify after taking the derivatives.
a.
f (x) = (x + 1) (x2 + x + 3).
b.
f (x) = (x2 + 7) (x3 2).
2.
Use quotient rule on the following. Dont simplify.
a.
h(x) =
b.
h(x) =
x2 +
MA 1170 Practice Test III
1.
Name
For the function f(x) = 3x4 4x3 + 1, nd the x- and y-coordinates of the critical points.
2.
For each of the following functions, nd the x-coordinate of the critical points, nd the signs of f , and
determine if each critic
MA 1170 Practice Final
Name
Final is at 10:15am on Monday, May 2nd.
1.
Consider the graph of some function f below.
f (x)
x
a.
Find limx1 f (x)
b.
Find limx1+ f (x)
c.
Find f (1).
d.
Is f continuous at x = 1?
e.
Find limx1 f (x)
f.
Find limx1+ f (x)
g.
Fi
MA 1170 Lecture 21 - Integration and Area
Friday, April 1, 2011
Objectives: Examine the relationship between the integral and area.
Area functions
Last time, I introduced a new notation for the derivative,
at the picture below.
dy
.
dx
This notation has s
MA 1170 Lecture 20 - Integration - Antiderivatives
Wednesday, March 30, 2011
Objectives: Introduce antidierentiation, sum, constant multiple rules.
Antiderivatives
Up to now, weve been working on the dierential side of calculus. Today, we will start looki
MA 1170 Lecture 17 - More on Absolute Maxs and Mins
Monday, March 21, 2011
Objectives: Determining maxs and mins over a closed interval
From last time, we saw that if we want to nd the maximum and minimum value of a function f over some
interval a x b, th
MA 1170 Lecture 18 - Exponential and Log Functions
Wednesday, March 23, 2011
Objectives: Introduce exponential and log functions and their derivatives
Exponential functions
Consider the function
(1)
f(x) = 2x .
This is an example of an exponential functio
MA 1170 Lecture 19 - Exponential Growth Model
Monday, March 28, 2011
Objectives: Explore application of exponential functions and population growth models.
The exponential growth model
Today, we will play with something called the exponential growth model
MA 1170 Lecture 16 - Absolute Maxs and Mins
Friday, March 18, 2011
Objectives: Determining maxs and mins over a closed interval
We know that relative maximums and minimums occur at critical points. Suppose we had a problem like
the following.
Weve got 100
MA 1170 Homework 14 Answers
For each of the given functions, nd the critical points, the signs of f , and for each critical points, determine
whether it is a relative maximum, relative minimum, or a saddle.
1.
f (x) = x2 3.
f (x) = 2x, so x = 0 is the onl
MA 1170 Practice Test I
1.
Name
Consider the function f(x) = x2 . Carefully plot at least ve points, and draw the graph.
1
MA 1170 Practice Test I
2
2.
In the graph of some function f below,
a.
estimate f(0.4) to two decimal places.
b.
estimate x, where f