Applications Of Derivatives Question 362
Question: The minimum value of $ 2x+3y, $ when $ xy=6, $ is
[MP PET 2003]
Options:
A) 12
B) 9
C) 8
D) 6
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=2x+3y $ when $ xy=6 $
$ f(x)=2x+3y=2x+\frac{18}{x} $
$ {f}’(x)=2-\frac{18}{x^{2}}=0 $
therefore $ x=\pm 3 $ and $ {f}’’(x)=\frac{36}{x^{3}}\Rightarrow {f}’’(3)>0 $
Putting $ x=+3 $ , we get the minimum value to be 12.
BETA
