MathDB

This function is nondecreasing (knowledge of calculus not required)

Source: Romania National Olympiad 2016, grade x, p.1

August 25, 2019

functioncalculusalgebra

Problem Statement

Let be a natural number

n\ge 2

and

n

positive real numbers

a_1,a_2,\ldots ,a_n

whose product is

1.

Prove that the function f:\mathbb{R}_{>0}\longrightarrow\mathbb{R} , f(x)=\prod_{i=1}^n \left( 1+a_i^x \right) , is nondecreasing.