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MATH1010:
Chapter 4 cont…
1
APPLICATIONS OF DERIVATIVES cont …
Maximum and Minimum Values (Section 4.1, pg. 279) cont…
Recall:
Last day, we looked at max and min values, but we explored this concept
graphically.
Example:
Sketch a graph of a continuous function
f
such that the absolute maximum of
)
(
x
f
on the interval (1, 1) does not exist and the absolute minimum equals 3.
Recall:
Last day, we discussed the Extreme Value Theorem which states that on a closed
interval, a continuous function attains both an absolute max and an absolute min.
Fermat’s Theorem:
If
f
has a local maximum or minimum at c, and if
)
(
c
f
′
exists,
then
0
)
(
=
′
c
f
.
Caution:
Some Important Points
Are all places where the derivative is zero a local max/min?
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View Full DocumentMATH1010:
Chapter 4 cont…
2
Do local max/min occur only at places where the derivative is zero?
Definition:
A
critical number
of a function
f
is a number
c
in the domain of
f
such that
either
0
)
(
=
′
c
f
or
)
(
c
f
′
does not exist.
So, rephrasing
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 Spring '08
 Kim
 Calculus, Derivative

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