Calc Midterm 4
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School
Rutgers University *
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Course
151
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
11
Uploaded by BailiffRockWolf28
RUTGERS
UNIV.
MIDTERM
QUIZ
©
2020
Suppose
that
f(x)
is
a
differentiable
function
with
f(7)=16
and
f'(7)=4.
Rutgers
Quiz
(vers.
d883s)
©
2020
(a)
Find
the
linearization
L(x)
of
f
centered
at
7.
Rutgers
Quiz
(vers.
d883s)
Rutgers
Quiz
(vers.
d883s)
©
2020
L(x)=
16
+4(x-7)
(b)
Use
the
standard
linear
approximation
to
find
an
estimate
to
f(6.93).
Do
not
round
your
answer.
Rutgers
Quiz
(vers.
d883s)
Rutgers
Quiz
(vers.
d883s)
Rutgers
Quiz
(vers.
d883s)
Rutgers
Quiz
(vers.
d883s)
f(6.93)~
15.72
.
Rutgers
Quiz
(vers.
d883s)
©
2020
RUTGERS
UNIV.
MIDTERM
QUIZ
©
2020
Question
is
complete.
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
©
2020
Find
the
absolute
maximum
and
minimum
values
of
f(x)
=
C-12
+
45x
-
64
on
the
interval
[2,4]
and
say
where
they
occur.
Rutgers
Quiz
(vers.
b245r)
Rutgers
Quiz
(vers.
b245r)
Rutgers
Quiz
(vers.
b245r)
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
©
2020
Rutgers
Quiz
(vers.
b245r)
(a)
f
has
an
absolute
maximum
of
-
10'.
The
absolute
maximum
occurs
at
the
x-value(s)
x=
3.
Rutgers
Quiz
(vers.
b245r)
(Use
commas
to
separate
values
as
needed.)
Rutgers
Quiz
(vers.
b245r)
(b)
f
has
an
absolute
minimum
of
—14
.
The
absolute
minimum
occurs
at
the
x-value(s)
x=
2.
Rutgers
Quiz
(vers.
b245r)
(Use
commas
to
separate
values
as
needed.)
RUTGERS
UNIV.
OFFICIAL
MATH
151
MIDTERM
©
2020
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
Rutgers
Quiz
(vers.
a807r)
©
2020
Use
the
graph
of
y
=
f'(x)
to
answer
questions
about
the
CONTINUOUS
FUNCTION
f.
(Note:
the
blobs
on
the
ends
of
the
graph
of
y
=f'(x)
are
arrows.)
Again,
the
graph depicted
above
is
for
y
=f'(x).
This
problem
has
parts
(a)-(f).
Rutgers
Quiz
(vers.
a807r)
©
2020
(a)
Find
the
critical
points
for
f.
The
critical
point(s)
for
f(x)
is/are
at
x=
-
1,5‘.
(Use
commas
to
separate
multiple
values,
if
needed.)
f
has
no
critical
points.
Rutgers
Quiz
(vers.
a807r)
©
2020
(b)
Find
the
interval(s)
where
f
is
increasing.
f(x)
is
increasing
on the
interval(s)
(5,
oo)‘.
(Use
interval
notation
and
separate
multiple
intervals
using
commas,
if
needed.)
fis
never
increasing.
Rutgers
Quiz
(vers.
a807r)
©
2020
1A\
Eind
tha
intansmalle)
whara
fie
danrancina
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
Rutgers
Quiz
(vers.
a807r)
©
2020
Use
the
graph
of
y
=
f'(x)
to
answer
questions
about
the
CONTINUOUS
FUNCTION
f.
(Note:
the
blobs
on
the
ends
of
the
graph
of
y
=f'(x)
are
arrows.)
Again,
the
graph depicted
above
is
for
y
=f'(x).
This
problem
has
parts
(a)-(f).
(c)
Find
the
interval(s)
where
f
is
decreasing.
f
is
never
decreasing.
f(x)
is
decreasing
on
the
interval(s)
(-
oo,
5)‘
(Use
interval
notation
and
separate
multiple
intervals
using
commas,
if
needed.)
Rutgers
Quiz
(vers.
a807r)
©
2020
(d)
Find
the
interval(s)
where
f
is
concave
up.
f
is
never
concave
up.
f(x)
is
concave
up on the
interval(s)
(-0,
=
1),
(3,
oo)‘
(Use
interval
notation
and
separate
multiple
intervals
using
commas,
if
needed.)
Rutgers
Quiz
(vers.
a807r)
©
2020
(e)
Find
the
interval(s)
where
f
is
concave
down.
Question
is
complete.
Tap
on
the red
indicators
to
see
incorrect
answers.
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