Question

Identify a counterexample to disprove n3 ≤ 3n2, where n is a real number.

Answer 1

`n^3\le3n^2\iff n^3-3n^2\le0\iff n^2(n-3)\le0`

The quantity on the left hand side will be positive for any
`n>3`, so suppose consider
`n=4`.

Now,


`4^3=64`

but


`3(4)^2=48`

and
`64\\ot\le48`