MATH 255A, Review for Midterm Test 3
Test topics
- Derivatives of the trigonometric functions (4.6).
- 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. Inflection points. 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).
- Absolute maxima and minima. Algorithm for finding
the absolute maximum/minimum, on bounded intervals (blue box on
p. 324) and unbounded intervals (cf. problems 31, 34, 6.1).
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).
Preparation for the test
Problems on the test will not be taken from the homework/practice
problems but they will be generally similar. The best way to
prepare is to study examples in the lectures and in the book
and to solve practice problems (think about how to solve it,
rather than look in the answer).
You could also check out the old Test 3 at
http://www.csun.edu/~panferov/math255a_f07/
General rules
Tests are closed books/notes.
Simple scientific calculator (example: TI-30XII) is allowed
on the test. Graphing calculators (example: TI-83, 84, 89)
may not be used. Calulator is not required to answer the
questions. You should justify all answers properly. Partial
credit will be given depending on how well you explain your
solutions. Correct answers without proper justification
will receive zero points.