Note: The exams may not have exactly three questions per
day.
If there are more questions, they’ll be easier
individually!
Sometimes finding antiderivatives is tricky:
An antiderivative of
f
(
x
) = (sin
x
) (
e
x
) is
..?..
(1/2) (sin
x
) (
e
x
) – (1/2) (cos
x
) (
e
x
).
Questions on section 4.7?
Questions on chapter 4?
Chapter Review true/false questions on page 248
#1: “If
f
′
(
c
) = 0, then
f
has a local maximum or minimum
at
c
.”
..?..
False; e.g., consider
f
(
x
) =
x
3
at
c
= 0.
If we knew that
f
′′
(
c
) was nonzero, we could conclude
that
f
has a local maximum or minimum at
c
.
#2: “If
f
has an absolute minimum value at
c
, then
f
′
(
c
) =
0.”
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..?..
False; e.g., consider
f
(
x
) = 
x
 at
c
= 0.
If we knew that
f
was differentiable at
c
, AND we knew
that
c
is not an endpoint, then we could conclude that
f
′
(
c
)
= 0.
#3: “If
f
is continuous on (
a
,
b
), then
f
attains an absolute
maximum value
f
(
c
) and an absolute minimum value
f
(
d
) at
some number
c
and
d
in (
a
,
b
).”
..?..
False; e.g., consider
f
(
x
) =
x
on (0,1).
The claim becomes true if we replace (
a
,
b
) by [
a
,
b
], by the
Extreme Value Theorem.
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 Fall '11
 Staff
 Calculus, Antiderivatives, Derivative, Rolle's theorem, absolute minimum value, Review true/false questions

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