MathDB

We will say that a point of the plane

(u, v)

lies between the parabolas

y = f(x)

and

y = g(x)

f(u) \leq v \leq g(u)

. Find the smallest real

p

for which the following statement is true: for any segment, the ends and the midpoint of which lie between the parabolas

y = x^2

and

y=x^2+1

, then they lie entirely between the parabolas

y=x^2

and

y=x^2+p

Problem Statement