Applications Of Derivatives Question 369
Question: The maximum value of xy when $ x+2y=8 $ is
[Kerala (Engg.) 2005]
Options:
A) 20
B) 16
C) 24
D) 8
E) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ x+2y=8 $ , $ y=\frac{8-x}{2} $
Now $ f(x)=xy=x.\frac{(8-x)}{2}=4x-\frac{x^{2}}{2} $
$ \therefore $ $ {f}’(x)=4-x $
For extremum, $ {f}’(x)=0 $
$ \therefore $ $ x=4 $ and y = 2.
Also $ {f}’’(x)=-1<0 $
So, maximum value of $ xy=4\times 2=8 $ .
BETA
