Question

Identify a counterexample to disprove n3 ≤ 3n^2, where n is a real number.
n = 2
n = −1
n = 0
n = 0.5

Answer 1

It's supposed to be n^3 < or equal to 3n^2.

Answer 2

just put the 4 values into the inequality

only one of them gives an incorrect result - but that proves the inequality is not true for all real numbers, as required

Answer 3

I did that and I got;
8<12=true
-1<3=true
0=0=true
.25<.75=false

Answer 4

So, it would be 0.5 but that's incorrect.

Answer 5

0.5 ^3 is not 0.25

Answer 6

however
0.125 <=0.75

so I believe 0.5 IS the correct answer

Answer 7

Okay, the computer must be incorrect then.

Answer 8

hold on a minute tho sorry...

Answer 9

0.5^3 =.125

so the inequality IS true

but it is also true for all the other answers

Answer 10

if x>3 then the inequality is false - but that is not an option

did oyu type the question correctly?

Answer 11

This is a screenshot of the exact problem, and the red arrow means that's the answer I picked and it was incorrect.

Answer 12

yeah - as I corrected myself - ALL the answers seem to give a correct solution to the inequality - so none is a 'counterexample'

any value x>3 IS a counterexample

Answer 13

hmm.. okay. Thank you.