Create assignment, 57321, Homework 22, Apr 18 at 1:41 pm
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CalC4c08c
50:03, calculus3, multiple choice,
<
1 min,
wordingvariable.
001
The graphs of the derivative of functions
f, g
and
h
are shown in
4
f
0
:
g
0
:
h
0
:
Use these graphs to decide which of
f, g
and
h
have a local minimum on (0
,
4)?
1.
only
f
and
g
correct
2.
only
f
3.
only
g
4.
only
h
5.
only
g
and
h
6.
only
f
and
h
7.
f, g,
and
h
Explanation:
By the First Derivative test, a differentiable
function
F
will have a
(i) a local maximum at
x
0
if
F
0
(
x
0
) = 0 and
the sign of
F
0
(
x
) changes from
positive
to
negative
as
x
passes through
x
0
;
(ii) a local minimum at
x
0
if
F
0
(
x
0
) = 0 and
the sign of
F
0
(
x
) changes from
negative
to
positive
as
x
passes through
x
0
.
When
F
0
is given by its graph, therefore, we
need to look for the
x
intercepts of the graph
of
F
0
and then check if the graph of
F
0
is
decreasing (for a local maximum) or increas
ing (for a local minimum) as the graph passes
through an
x
intercept.
Applying these criteria to
f, g
and
h
we see
that the graphs of all of
f
0
, g
0
and
h
0
cross the
x
axis at least once in (0
,
4), but because of
the way these graphs change sign
only
f
and
g
have a local minimum on (0
,
4).
keywords:
local maximum, first derivative
test, graph, local extrema
CalC4c18c
50:03, calculus3, multiple choice,
<
1 min,
wordingvariable.
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 Spring '06
 McAdam
 Calculus, Derivative, Riemann, 1 min

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