MathDB

We are given a finite number of functions of the form

y = c2^{-|x-d|}

. In each case

c

and

d

are parameters with

c > 0

. The function

f(x)

is defined on the interval

[a, b]

as follows: For each

x

[a, b]

f(x)

is the maximum value taken by any of the given functions

y

(defined above) at that point

x

. It is known that

f(a) = f(b)

. Prove that the total length of the intervals in which the function

f

is increasing is equal to the total length of the intervals in which it is decreasing (that is, both are equal to

(b- a)/2

).
(NB Vasiliev)

Problem Statement