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Chapter Four: Applications of Differentiation
Chapter Three showed us several techniques to differentiate a function. Chapter
Four is going to show us several applications that involve the derivative.
Definition:
Extrema
Let f be defined on an interval containing c.
1.
( )
f c
is the
minimum
of f on I if
( ) ( )
f c
f
x
≤
for all x in I.
2.
( )
f c
is the
maximum
of f on I if
( ) ( )
f c
f
x
≥
for all x in I.
The minimum and maximum of a function f on an interval are called the
extreme
values,
or
extrema
of the function on the interval.
If I is equal to the domain of the function, then the minimum and maximum are
called
absolute.
•
If a function has a “peak,” the y – value where the peak happens is called a
relative maximum
. If a function has a “valley,” the y – value where the valley
happens is called the
relative
minimum.
•
All absolute extrema on an open interval are relative extrema, but not all
relative extrema are absolute extrema.
Definition:
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 Summer '11
 MarioBorha
 Calculus, Derivative

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