Proving 3x^2 + x^3 > 0 for x ≥ -1

[silvermane]

Homework Statement

We have x greater or equal to -1, and
(1+x)^3 greater/equal to 1 +3x.
We need to prove that 3x^2 +x^3 is greater or equal to zero for x greater/equal to -1.

The Attempt at a Solution

I've simplified the inequality to 3x^2 greater/equal to 0, but now I need to show that this simplified inequality is true for x greater/equal to -1. I'm almost there, but need some guidance. Thanks for all your help in advance!

 

[Ryker]

Just a thought, but perhaps you can do it on a case-by-case basis, the first case being $$x > 0$$ and the second $$-1 \le x < 0$$. But I don't think this inequality is true for all x.

edit: Damn, can you see my LaTeX code or does it just show as an explanation that it is such?

 

[silvermane]

edit: Damn, can you see my LaTeX code or does it just show as an explanation that it is such?

I can't see any of your code :(

Edit: I'm trying to prove it true for x greater/equal to -1 though

 

[Ryker]

Alright, I fixed the code.

 

[silvermane]

Okay, that works :) thank you!

 

[Vanadium 50]

Expand (1+x)^3. See where that gets you.

 

[Vanadium 50]

Alternatively, factor out an x^2.

 

[silvermane]

Alternatively, factor out an x^2.

I've completely factored and broke it into cases. Thanks for the help!