can someone help me with my assignment
Find two numbers whose sum is a, if the product of the square of one by the cube of the other is maximum.
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Answer:
Let the ture positive numbers be x,(x,y>0)
x+y=20 - Given
We need to maximise x2y3
x=20−y
f(y)=y3(20−y)2
for minimum
f′(y)=0
3y2(20−y)2+y32(20−y)(−1)=0
3y2(20−y)2−2y3(20−y)=0
y2(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 x2y3 maximum
Step-by-step explanation:
hope this will help
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