Question

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

n=-1
n=0
n=4
n=0.5

thanks you

Answer 1

geez -- did you even bother trying the choices?
clearly, -1^3 is negative, and 3*1^2 is positive, so ✅

Now , in general, if
n^3 ≤ 3n^2
n^2 (n-3) ≤ 0
and since n^2 is never negative, that means
n-3 ≤ 0
n ≤ 3

Answer 2

Did you mean:
n^3 ≤ 3n^2 ?

let n = 5
is 5^3 ≤ 3(5)^2 ?
is 125 ≤ 75 ? , obviously NO

so your hypothesis is bogus, (all you need is one counterexample)