The product of three non negative number whose sum is 1, is maximum at the poitn
Answers
Answered by
0
Let's call the first number
x
Then the other will be
9
−
x
(as they add up to
9
So the question translates to:
Find the maximum of
y
=
x
2
(
9
−
x
)
=
9
x
2
−
x
3
The maximum is when the derivative is set to
0
y
'
=
18
x
−
3
x
2
=
3
x
⋅
(
6
−
x
)
=
0
→
x
=
6
And the other number will be
9
−
6
=
3
Check the answer:
6
2
⋅
3
=
108
To be sure that this is a maximum you could check for:
5.9
↔
3.1
and for
6.1
↔
2.9
Similar questions