Section 3.1
Derivatives of Polynomials and Exponential Functions
Goals
Learn formulas for the derivatives of
Constant functions Power functions Exponential functions
Constant Functions
The graph of the constant function f(x) = c is the horizo
Section 2.1
The Tangent and Velocity Problems
Goals
Use two problems to explain the need for the notion of limit:
The tangent problem The velocity problem What would it mean in general for a line to be tangent to a curve?
Tangent Problem
touchi
Section 1.1
Four Ways to Represent a Function
Goals
Learn to represent functions using
Words Tables of values Graphs Formulas
Section 1.1
Four Ways (cont'd)
Discuss piecewise defined functions, including the absolute value function Study s
TRIGONOMETRY
DEFINITIONS:
tan x = sin x ; cos x
sec x =
1 , cos x
csc x =
1 , sin x
cot x =
cos x sin x
FUNDAMENTAL FORMULAS:
cos 2 x + sin 2 x = 1 , 1 + tan 2 x = sec 2 x , 1 + cot 2 x = csc 2 x
DERIVATIVES:
d (sin x) = cos x dx d (csc x) =
Section 4.6
Steps For Optimization Problems
We can adapt the problem-solving principles discussed earlier to give these steps for solving optimization problems:
1. Understand the Problem Read the problem until it is clearly understood. Ask yourself
Section 4.5
Indeterminate Forms and l'Hospital's Rule
Goals
Introduce the various types of indeterminate forms Find limits of indeterminate forms using l'Hospital's Rule.
Introduction
Suppose we want to analyze the behavior of the function F (
Section 4.3
Derivatives and the Shape of Curves
Goals
Apply the Mean Value Theorem to finding where functions are increasing and decreasing Discuss the
first derivative test and second derivative test
Mean Value Theorem
This theorem is the ke
Section 4.2
Maximum and Minimum Values
Goals
Solve problems requiring the minimum or maximum value of a quantity Study absolute vs. local maxima/minima of a function Introduce the Extreme Value Theorem and Fermat's Theorem, as well as critical p
CONCEPTS TO MEMORIZE:
Limit:
lim f (x) = L means that f(x) can made as close to L as we want, when x is very close to a.
x a x a
x a
lim f (x) = means that f(x) can made arbitrary large, when x is made very close to a.
lim f (x) = - means that f(x)