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Acceleration and the Second
Derivative
The
acceleration
of a moving object is the
derivative of its velocity (the
second
derivative
of the position function.)
Function notation:
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View Full Document Second Derivative
Concavity
Let
f
be a differentiable function on (
a
,
b
).
concave upward
concave downward
1.
f
is
concave upward
on (
a
,
b
) if
is increasing on (
a
,
b
).
That is,
for each value of
x
in (
a
,
b
).
2.
f
is
concave downward
on (
a
,
b
) if
is decreasing on (
a
,
b
).
That is,
for each value of
x
in (
a
,
b
).
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View Full Document Inflection Point
A point on the graph of
f
at which concavity changes
is called an
inflection point
.
To find inflection points, find any point,
c
, in the
domain where
is undefined.
changes sign from the left to the right of
c,
If
then (
c,f
(
c
))
is an inflection point of
f
.
The Point of Diminishing Returns
Let
S
be a sales function.
Where the graph of
S
is concave
up, monthly sales are increasing; more units are being sold
each month than the month before.
Where the graph of
S
is concave down, monthly sales are decreasing; fewer units
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This note was uploaded on 09/09/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.
 Spring '11
 Staff
 Calculus, Derivative

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