MathDB

Consider all cubic polynomials

f(x)

such that

f(2018)=2018

, the graph of

f

intersects the

y

-axis at height

2018

, the coefficients of

f

sum to

2018

, and

f(2019)>(2018)

.
We define the infinimum of a set

S

as follows. Let

L

be the set of lower bounds of

S

. That is,

\ell\in L

if and only if for all

s\in S

\ell\leq s

. Then the infinimum of

S

\max(L)

.
Of all such

f(x)

, what is the infinimum of the leading coefficient (the coefficient of the

x^3

term)?

Problem Statement