Which of the following functions has a graph that is a line?
f(x) = x
f(x) = x 2
f(x) = |x|
Answers
Answer:
The slope of the tangent line of a graph
y
=
f
(
x
)
at a point
x
0
is given by the derivative of
f
at that point, that is,
f
'
(
x
0
)
.
A horizontal tangent line implies a slope of
0
, so our goal is to find the points at which the derivative
f
(
x
)
evaluates to
0
.
Using the quotient rule, we find the derivative as
f
'
(
x
)
=
d
d
x
x
2
x
−
1
=
(
x
−
1
)
(
d
d
x
x
2
)
−
x
2
(
d
d
x
(
x
−
1
)
)
(
x
−
1
)
2
=
2
x
(
x
−
1
)
−
x
2
(
1
)
(
x
−
1
)
2
=
2
x
2
−
2
x
−
x
2
(
x
−
1
)
2
=
x
2
−
2
x
(
x
−
1
)
2
=
x
(
x
−
2
)
(
x
−
1
)
2
Setting this equal to zero, we get
x
(
x
−
2
)
(
x
−
1
)
2
=
0
⇒
x
(
x
−
2
)
=
0
⇒
x
=
0
or
x
=
2
Thus, the graph of
f
(
x
)
has a horizontal tangent line at
x
=
0
and
x
=
2
, that is, at the points
(
0
,
0
)
,
(
2
,
4
)
Step-by-step explanation:
Hope it works out for you
Answer:
f(x) = x
Step-by-step explanation:
because it is linear function. and the graph of a linear function is always a line.