C (although it is neither increasing nor decreasing at x = 0)
All the other ones are decreasing for part of the domain.
Thus there is no way to prove this one way or the other.
You can simply draw the graphs and see the answer. But that is hardly a poof.
On the other hand, with calculus we can see which one has a non-negative derivative. That would prove it.
Why don't you just graph the function? To rigorously prove it, we note that its derivative is 9x^2, which is always non-negative. Therefore the function in (C) is always increasing (except when x = 0, where the derivative is zero).
The the statement that is an increasing function means that if then .
That is clearly true in this case. When I made the remark reply #3 about proof, it was addressing the fact that this is a precalculus forum.
There is of course a perfectly good way of proving this.
Suppose that then then . Proved.