Asked by edward
12 is divided into two parts such that the product of the square of one part and fourth power of the other give a maximum,find the two numba
Answers
Answered by
Steve
x+y=12
z = x^2 y^(1/4)
= (12-y)^2 y^1/4
= 144y^1/4 - 24 y^5/4 + y^9/4
dz/dy = 36/y^3/4 - 30y^1/4 + 9/4 y^5/4
= (36 - 30y + 9/4 y^2) / y^3/4
dz/dy=0 when
9y^2-120y+144 = 0
3(3y-4)(y-12) = 0
clearly, y=12 gives z=0, a minimum
y=3/4 gives x=45/4 and z=(1024/9) 4throot(4/3)
z = x^2 y^(1/4)
= (12-y)^2 y^1/4
= 144y^1/4 - 24 y^5/4 + y^9/4
dz/dy = 36/y^3/4 - 30y^1/4 + 9/4 y^5/4
= (36 - 30y + 9/4 y^2) / y^3/4
dz/dy=0 when
9y^2-120y+144 = 0
3(3y-4)(y-12) = 0
clearly, y=12 gives z=0, a minimum
y=3/4 gives x=45/4 and z=(1024/9) 4throot(4/3)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.