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Mathematics
Mathematics
Problem
If
f
(
x
)
=
x
2
−
2
∣
x
∣
f(x) = x^2 - 2|x|
f
(
x
)
=
x
2
−
2∣
x
∣
and
g
(
x
)
=
{
min
{
f
(
t
)
}
:
−
2
≤
t
≤
x
,
−
2
≤
x
≤
0
max
{
f
(
t
)
}
:
0
≤
t
≤
x
,
0
≤
x
≤
3
g(x) = \begin{cases} \min\{f(t)\} : -2 \le t \le x, -2 \le x \le 0 \\ \max\{f(t)\} : 0 \le t \le x, 0 \le x \le 3 \end{cases}
g
(
x
)
=
{
min
{
f
(
t
)}
:
−
2
≤
t
≤
x
,
−
2
≤
x
≤
0
max
{
f
(
t
)}
:
0
≤
t
≤
x
,
0
≤
x
≤
3
(i) Draw the graph of
f
(
x
)
f(x)
f
(
x
)
and discuss its continuity and differentiability. (ii) Find and draw the graph of
g
(
x
)
g(x)
g
(
x
)
. Also, discuss the continuity.
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