Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm in need of some help putting together this proof. I'm not sure if it's just harder than it looks, or I need to spend more time learning how to put them together.

1. The problem statement, all variables and given/known data

Show that [itex]f(x) = 9x^2 + 3x[/itex] is strictly increasing on the interval [itex](0, 10][/itex]

2. Relevant equations

3. The attempt at a solution

I realise there are various arguments involving the turning point of a quadratic equation, but I don't think this is the type of answer that they're looking for.

Let [itex]u < v[/itex] be two elements of the interval [itex](0, 10][/itex]. Then from [itex]f(u) < f(v)[/itex] we obtain:

[tex]9u^2 + 3u < 9v^2 + 3v[/tex],

[tex]9u^2 + 3u - 9v^2 + 3v < 0[/tex]

From here, I think I need to get to [itex]u < v[/itex], but I can't see how to do it.

Thanks for any help.

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

Dismiss Notice

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!

# Show that a function is increasing

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