MathDB

Let

f:\mathbb{R}\rightarrow\mathbb{R}

be a function defined as the maximum of a finite number of functions

g:\mathbb{R}\rightarrow\mathbb{R}

of the form

g(x)=C\cdot10^{-|x-d|}

(with different values of parameters

d{}

and

C>0

). For real numbers

a<b

we have

f(a)=f(b)

. Prove that on the segment

[a;b]

the sum of legnths of segments on which

f

is increasing is equal to the sum of legnths of segments on which

f

is decreasing.

Problem Statement