Differentiable Function Identity and Limit (Jee… | ExamDuo
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Chain Rule and Composite Functions
Hard
Differentiable Function Identity and Limit
Suppose a differentiable function
f
(
x
)
satisfies the identity
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
x
y
2
+
x
2
y
for all real
x
and
y
.
If
lim
x
→
0
f
(
x
)
x
=
1
,
then
f
′
(
3
)
is equal to _______.
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