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VTRMC
2009 VTRMC
Problem 7
Problem 7
Part of
2009 VTRMC
Problems
(1)
existence of DE solution
Source: VTRMC 2009 P7
5/31/2021
Does there exist a twice differentiable function
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
such that
f
′
(
x
)
=
f
(
x
+
1
)
−
f
(
x
)
f'(x)=f(x+1)-f(x)
f
′
(
x
)
=
f
(
x
+
1
)
−
f
(
x
)
for all
x
x
x
and
f
′
′
(
0
)
≠
0
f''(0)\ne0
f
′′
(
0
)
=
0
? Justify your answer.
differential equations
calculus