given the function f(x) = m+c . identify the statement that is false
Answers
Answer:
Answer the following questions.
For each of the following ten statements answer TRUE or FALSE as appropriate:
If
f
is differentiable on
[
−
1
,
1
]
then
f
is continuous at
x
=
0
.
If
f
′
(
x
)
<
0
and
f
"
(
x
)
>
0
for all
x
then
f
is concave down.
The general antiderivative of
f
(
x
)
=
3
x
2
is
F
(
x
)
=
x
3
.
ln
x
exists for any
x
>
1
.
ln
x
=
π
has a unique solution.
e
−
x
is negative for some values of
x
.
ln
e
x
2
=
x
2
for all
x
.
f
(
x
)
=
|
x
|
is differentiable for all
x
.
tan
x
is defined for all
x
.
All critical points of
f
(
x
)
satisfy
f
′
(
x
)
=
0
.
Answer each of the following either TRUE or FALSE.
The function
f
(
x
)
=
{
3
+
sin
(
x
−
2
)
x
−
2
if
x
≠
2
3
if
x
=
2
is continuous at all real numbers
x
.
If
f
′
(
x
)
=
g
′
(
x
)
for
0
<
x
<
1
,
then
f
(
x
)
=
g
(
x
)
for
0
<
x
<
1
.
If
f
is increasing and
f
(
x
)
>
0
on
I
,
then
g
(
x
)
=
1
f
(
x
)
is decreasing on
I
.
There exists a function
f
such that
f
(
1
)
=
−
2
,
f
(
3
)
=
0
,
and
f
′
(
x
)
>
1
for all
x
.
If
f
is differentiable, then
d
d
x
f
(
√
x
)
=
f
′
(
x
)
2
√
x
.
d
d
x
10
x
=
x
10
x
−
1
Let
e
=
exp
(
1
)
as usual. If
y
=
e
2
then
y
′
=
2
e
.
If
f
(
x
)
and
g
(
x
)
are differentiable for all
x
,
then
d
d
x
f
(
g
(
x
)
)
=
f
′
(
g
(
x
)
)
g
′
(
x
)
.
If
g
(
x
)
=
x
5
,
then
lim
x
→
2
g
(
x
)
−
g
(
2
)
x
−
2
=