Section 2.1: Using First Derivatives to Find Maximum and Minimum Values and
Sketch Graphs
OBJECTIVE
Find relative extrema using the First-Derivative Test.
Sketch graphs of continuous functions.
DEFINI
3.1: Exponential Functions
OBJECTIVE
Graph exponential functions.
Differentiate exponential functions.
DEFINITION:
Exponential Functions
For a > 0 , a 0 , and all real numbers x
() =
Defines the expo
Section 2.2: Using Second Derivatives to Find Maximum and Minimum Values and
Sketch Graphs
OBJECTIVE
Find the relative extrema of a function using the Second-Derivative Test.
Graph a continuous functi
2.4: Using Derivatives to Find Absolute Maximum and Minimum Values
OBJECTIVE
Find absolute extrema (also called global extremes)
Example 1:
() = 2 4 + 5
Find the critical points and relative max/min p
2.5: Maximum-Minimum Problems; Business and Economics Applications
OBJECTIVE
Solve maximum and minimum problems using calculus.
A Strategy for Solving Maximum-Minimum Problems
1. Read the problem care
1.5: Differentiation Techniques: The Power and Sum-Difference Rules
OBJECTIVE
Differentiate using the Power Rule or the Sum-Difference Rule.
Differentiate a constant or a constant times a function.
De
1.8: Higher Order Derivatives
OBJECTIVE
Find derivatives of higher order.
Given a formula for distance, find velocity and acceleration.
Consider the function given by = () = 5 3 4 +
Its derivative f
1.7: The Chain Rule
OBJECTIVE
Find the composition of two functions.
Differentiate using the Extended Power Rule or the Chain Rule.
THEOREM 7: The Extended Power Rule
Suppose that g(x) is a differenti
1.4: Differentiation Using Limits of Difference Quotients
OBJECTIVE
Find derivatives and values of derivatives
Find equations of tangent lines
DEFINITION: The slope of the tangent line at (, () is
=
1.3: Average Rates of Change
OBJECTIVE
Compute an average rate of change.
Find a simplified difference quotient.
DEFINITION: The average rate of change of y with respect to x, as x changes from x1 to