Download 3.1 Extreme Values

3.1 Extreme Values
•Absolute or Global
Maximum
•Absolute or Global
Minimum
3.1 Extreme Values
•Local or Relative
Maximum
•Local or Relative
Minimum
Ex 1: Identify all extrema.
a
b
c
d e
fg
Ex 1: Identify all extrema.
a
b
c
d e
fg
Ex 1: Identify all extrema.
a
b
c
d e
fg
Ex 1: Identify all extrema.
a
b
c
d e
fg
3.1 Extreme Values
•A critical number of f
is a number c in the
domain of f such
that either f (c) = 0
or f (c) does not
exist.
Ex 2: Find the critical
numbers of g.
g x   x 4  x
•Extreme Value Thm:
If f is continuous on a
closed interval [a, b],
then f attains an absolute
max & absolute min at
some x-values on [a, b]
To find Absolute Max’s &
Min’s on a closed interval:
1) Find f  & all critical numbers.
2) Find the value of f at each
critical number.
3) Find the value of f at each
endpoint.
4) Smallest = Absolute Min
5) Largest = Absolute Max
Ex 3: Find the absolute
max & min values of
the function on the
interval: ½  x  4
f  x   x  3x  1
3
2
HW – 3.1 pg. 169
# 1, 2, 3 – 7 odds,
# 9 – 12 all,
# 13 – 41 EOO