MathDB

Let

S \subset [0, 1]

be a set of 5 points with

\{0, 1\} \subset S

. The graph of a real function

f : [0, 1] \to [0, 1]

is continuous and increasing, and it is linear on every subinterval

I

[0, 1]

such that the endpoints but no interior points of

I

are in

S

.
We want to compute, using a computer, the extreme values of

g(x, t) = \frac{f(x+t)-f(x)}{ f(x)-f(x-t)}

for

x - t, x + t \in [0, 1]

. At how many points

(x, t)

is it necessary to compute

g(x, t)

with the computer?

11