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Problems
If
f
(
x
)
=
{
x
(
e
4
/
x
−
e
−
4
/
x
e
4
/
x
+
e
−
4
/
x
)
,
x
≠
0
0
,
x
=
0
f(x) = \begin{cases} x \left( \frac{e^{4/x} - e^{-4/x}}{e^{4/x} + e^{-4/x}} \right), & x \ne 0 \\ 0, & x = 0 \end{cases}
f
(
x
)
=
{
x
(
e
4/
x
+
e
−
4/
x
e
4/
x
−
e
−
4/
x
)
,
0
,
x
=
0
x
=
0
…
Mathematics
Problem
If
f
(
x
)
=
{
x
(
e
4
/
x
−
e
−
4
/
x
e
4
/
x
+
e
−
4
/
x
)
,
x
≠
0
0
,
x
=
0
f(x) = \begin{cases} x \left( \frac{e^{4/x} - e^{-4/x}}{e^{4/x} + e^{-4/x}} \right), & x \ne 0 \\ 0, & x = 0 \end{cases}
f
(
x
)
=
{
x
(
e
4/
x
+
e
−
4/
x
e
4/
x
−
e
−
4/
x
)
,
0
,
x
=
0
x
=
0
, then at
x
=
0
x = 0
x
=
0
,
f
(
x
)
f(x)
f
(
x
)
is a. differentiable b. not differentiable c.
f
′
(
0
)
=
−
1
f'(0) = -1
f
′
(
0
)
=
−
1
d.
f
′
(
0
)
=
1
f'(0) = 1
f
′
(
0
)
=
1
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