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natalie2sheffield
01.10.2019 •
Mathematics
If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so that the product of the first and cube of the second is a maximum.
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Ответ:
x=(60-3y)/2
p=xy^3, using x from above:
p=y^3(60-3y)/2
p=(60y^3-3y^4)/2
dp/dy=(180y^2-12y^3)/2
dp/dy=90y^2-6y^2
dp/dy=0 when:
90y^2-6y^3=0
6y^2(15-y)=0, we know y>0 so
y=15, since x=(60-3y)/2
x=7.5
(We solved it this way because otherwise you get quartic equations and cubic derivatives, yuck :P)
Ответ:
2.5
Step-by-step explanation:
its the middle point