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Mathematics
Mathematics
Problem
If
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
∣
x
∣
y
+
x
y
2
f(x+y) = f(x) + f(y) + |x|y + xy^2
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
∣
x
∣
y
+
x
y
2
,
∀
x
,
y
∈
R
\forall x, y \in \mathbb{R}
∀
x
,
y
∈
R
and
f
′
(
0
)
=
0
f'(0) = 0
f
′
(
0
)
=
0
, then a.
f
f
f
need not be differentiable at every non-zero
x
x
x
b.
f
f
f
is differentiable for all
x
∈
R
x \in \mathbb{R}
x
∈
R
c.
f
f
f
is twice differentiable at
x
=
0
x = 0
x
=
0
d. None of the above
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