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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
∫
0
x
∣
t
∣
d
t
f(x) = \int_{0}^{x} |t| dt
f
(
x
)
=
∫
0
x
∣
t
∣
d
t
, then a.
f
(
x
)
f(x)
f
(
x
)
is continuous but not differentiable for all
x
∈
R
x \in R
x
∈
R
b.
f
(
x
)
f(x)
f
(
x
)
is continuous and differentiable for all
x
∈
R
x \in R
x
∈
R
c.
f
(
x
)
f(x)
f
(
x
)
is continuous for
x
∈
R
−
{
1
2
}
x \in R - \left\{\frac{1}{2}\right\}
x
∈
R
−
{
2
1
}
and
f
(
x
)
f(x)
f
(
x
)
is differentiable for
x
∈
R
−
{
1
2
}
x \in R - \left\{\frac{1}{2}\right\}
x
∈
R
−
{
2
1
}
d. None of these
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