Applications Of Derivatives Question 361
Question: If $ x-2y=4, $ the minimum value of $ xy $ is
[UPSEAT 2003]
Options:
A) - 2
B) 2
C) 0
D) - 3
Show Answer
Answer:
Correct Answer: A
Solution:
$ x-2y=4 $
therefore $ x=2y+4 $ –(i) Let $ P=xy $
From (i), $ P=y(2y+4)=4y+2y^{2} $ ; $ \frac{dP}{dy}=4+4y=0 $
$ y=-1\Rightarrow x=2 $ and $ \frac{d^{2}P}{dy^{2}}=4 $ (+ve) \ $ {P _{min\text{.}}}=xy=(2),(-1)=-2 $ .
BETA
