Divide the number 20 in two positive integers such that the product of square of one and cube of other is maximum.
{{{❤_ GOOD AFTERNOON GUY'S _❤}}}
Attachments:
Answers
Answered by
2
Let the ture positive numbers be x,(x,y>0)
x+y=20 - Given
We need to maximise x
2
y
3
x=20−y
f(y)=y
3
(20−y)
2
for minimum
f
′
(y)=0
3y
2
(20−y)
2
+y
3
2(20−y)(−1)=0
3y
2
(20−y)
2
−2y
3
(20−y)=0
y
2
(20−y)(3(20−y)−2y)=0
60−3y−2y=0 y
=0&y
=20
y=12 if y=20 then x=0 which does not
x=8 make the x
2
y
3
maximum
Be happy always ☺️☺️☺️
l hope it will help u ☺️☺️☺️
Attachments:
Similar questions