MHB Checking if f(x)=x^3 is Monotonic: No Derivatives Needed

[Yankel]

Hello,

I want to check if

f(x)=x^3 is monotonically increasing or monotonically decreasing or not monotonic at all.

How do I do that, without using derivatives yet ?

Thanks !

 

[Evgeny.Makarov]

You use the definition.

 

[MarkFL]

Let $h$ be some positive real number, then if:

$$f(x+h)-f(x)\ge0$$ the function is monotically increasing or if:

$$f(x+h)-f(x)\le0$$ the function is monotically decreasing.