The sum of the two numbers is 8 what will be the maximum value of the sum of their reciprocals
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Answer:
1/2
Step-by-step explanation:
Let one number be x and the other be 8-x
S(sum of reciprocals)=1/x + 1/8-x
dS/dx= -8(8-2x)/(8x-x^2)^2 [not including steps of derivation]
dS/dx=0
8-2x=0
=>x=4
to prove its maximum, find second derivative and substitute value of x and show d^2S/dx^2<0
=> maximum value of sum of reciprocals=1/4+1/4=>1/2
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