MATH 255A, Review Sheet for Test 3
Course website:
http://www.csun.edu/~panferov/math255a/
Test topics
- Increasing and decreasing functions.
Type of problem: find the intervals on which
the function increases/decreases, using the
first derivative (5.1).
- Critical points. Relative (local) extrema.
First and second derivative tests.
Type of problem: find the locations and the values of the
local extrema (max and min) (5.2, 5.3).
- The higher derivatives. The second derivative; convex
and concave functions. Types of problems: find a derivative
of order higher than one. Find the intervals of
convexity/concavity, and the inflection points (5.3).
- Curve sketching, using the first and second derivative.
For the steps see lecture notes or page 306
in the book. Type of problem: sketch the graph of a
function (5.4).
- Global (absolute) maxima and minima. Algorithm for finding
the maximum and minimum on a closed bounded interval
(blue box on p. 324).
Modifications for an infinite interval (6.1).
- Applications. Word problems on maxima and minima (6.2).
Background material
Everything that was listed in the topics of Test 1
and Test 2, particularly
- The derivatives of the following functions, xn,
√x, 1/x,
emx, sin(x), cos(x), ln x, ln|x|.
- All rules of differentiation from Test 2.
- Properties of exponential, logarithmic, and
trigonometric functions (2.1,
2.2, 2.4), and their graphs.
Radian measure and values of trig. functions
for special angles: 0, π/6, π/4,
π/3, π/2, 2π/3, etc. (2.4).
- Formulas for the area and volume as appear in problems with applications.
Practice tests
Here are two examples of practice tests compiled of problems
from the textbook.
5.1: 38, 5.2: 22, 44, 5.3: 24, 5.4: 10,
6.1: 18, 6.2: 24.
5.1: 21, 5.2: 27, 5.3: 9, 39, 5.4: 9,
6.1: 17, 6.2: 25.
Answers to even-numbered problems can
be found here.
You should also review problems in the last two Homework Assignments.
More problems can be found in the review sections to Chapters 5 and 6,
see the Detailed Schedule.
General rules
Same as for Test 1 and Test 2.