(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]Let F(x) = (x-a)^2(x-b)^2 + x[/tex]. Show that the output [tex]\frac{a+b}{2}[/tex] exists for some value x.

2. Relevant equations

Quadratic formula. [tex]x^2 \geq 0[/tex].

3. The attempt at a solution

Hmm I've tried setting the two equal but that doesn't look nice (if I multiply everything out). It's easy to find the zeros of F(x) so there might be someway to relate to that? If someone could just give me a hint at a good first step for showing the existence of a certain output of a function.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving existence

**Physics Forums | Science Articles, Homework Help, Discussion**