Chapter 7 Curve Sketching
7.2 CRITICAL POINTS, LOCAL MAXIMA AND LOCAL
MINIMA
Terms:
1. Local minimum values: if f(x) changes from negative to zero
to positive as x increases from x<a to x>a, then (a, f(a) is a
local minimum. It always occurs at the critic
Chapter 7 Curve Sketching
7.3 VERTICAL AND HORIZONTAL ASYMPTOTES
Vertical Asymptotes:
EXAMPLE: Determine the vertical asymptote of the function and describe the end
behavior of the graph near the asymptote.
x2 + x 2 =0
(x+2) (x-1) = 0
Equations of the asy
Chapter 7 Curve Sketching
7.4 CONCAVITY AND POINTS OF INFLECTION
Terms:
1. Concave up: the graph of y = f(x) is concave up on the interval if
all the tangents in the interval are increasing. The second
derivative is positive.
2. Concave down: the graph of
Chapter 7 Curve Sketching
7.1 INCREASING AND DECREASING FUNCTIONS
Increasing and Decreasing intervals
Using the derivative to find the increasing and decreasing intervals
For a continuous and a differential function f, we can use the
derivative f( x) to d