Applications Of Derivatives Question 34
Question: The maximum value of xy subject to $ x+y=8 $ , is
[MNR 1995]
Options:
A) 8
B) 16
C) 20
D) 24
Show Answer
Answer:
Correct Answer: B
Solution:
$ x+y=8; $
$ \therefore y=8-x $ …..(i) Now $ f(x)=xy=x(8-x)=8x-x^{2} $ ,
$ \therefore {f}’(x)=8-2x $ For maximum value of $ f(x),,f’(x)=0 $
$ \therefore $ $ x=4 $ and $ y=4 $
So, maximum value of $ xy=4\times 4=16 $ .
BETA
