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Problems
Let
f
(
x
)
=
{
min
{
x
,
x
2
}
,
x
≥
0
max
{
2
x
,
x
2
−
1
}
,
x
<
0
f(x) = \begin{cases} \min\{x, x^2\}, & x \geq 0 \\ \max\{2x, x^2 - 1\}, & x < 0 \end{cases}
f
(
x
)
=
{
min
{
x
,
x
2
}
,
max
{
2
x
,
x
2
−
1
}
,
x
≥
0
x
<
0
…
Mathematics
Problem
Let
f
(
x
)
=
{
min
{
x
,
x
2
}
,
x
≥
0
max
{
2
x
,
x
2
−
1
}
,
x
<
0
f(x) = \begin{cases} \min\{x, x^2\}, & x \geq 0 \\ \max\{2x, x^2 - 1\}, & x < 0 \end{cases}
f
(
x
)
=
{
min
{
x
,
x
2
}
,
max
{
2
x
,
x
2
−
1
}
,
x
≥
0
x
<
0
Then which of the following is not true? (a)
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
0
x = 0
x
=
0
(b)
f
(
x
)
f(x)
f
(
x
)
is not differentiable at
x
=
1
x = 1
x
=
1
(c)
f
(
x
)
f(x)
f
(
x
)
is not differentiable at exactly three points (d) None of these.
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