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divide 64 into two parts such that the sum of the cubes of two parts is minimum

divide 64 into two parts such that the sum of the cubes of two parts is minimum
 

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
9 years ago
let two parts are x and 64-x
then S= x3+(64-x)3
dS/dx=3x2+3(64-x)2(-1)
for maxima or minima ds/sx must be zero
so put ds/sx=0
3[x2-(64-x)2]=0
=> x=32
d2S/dx2=6x+3(2)(64-x)
put x= 32 , then d2s/dx2= 6(32)+6(64-32)=384 >0
so S is minima at x=32
so the parts are 32, 64-32 i.e 32, 32
Ans. 32,32
Thanks & Regards
Rinkoo Gupta
AskIItians Fcaulty

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