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The minimum value of 2x + 3y, when xy = ...

The minimum value of `2x + 3y`, when `xy = 6` is

A

9

B

12

C

8

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=2x+3y`
`impliesf(x)=2x+18/x [ :' xy=6` given `]`
`:.f'(x)=2-18/(x^(2))`
For maxima or minima put `f'(x)=0`
`implies0=2-18/(x^(2))impliesx=+-3`
and `f''(x)=36/(x^(3))`
At `x=3,f''(3)=36/(3^(3))gt0`
`:.` At `x=3, f(x)` is minimum.
The minimum value is `f(3)=12`.
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