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Question

If ab=2a+3b,a>0,b>0 then the minimum value of ab is


A

12

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B

24

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C

14

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D

None of these

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Solution

The correct option is B

24


Explanation for the correct option:

Find the minimum value of ab:

Given, ab=2a+3b

(a3)b=2a

b=2aa3

Let z=ab

=a×2aa-3=2a2a3

Step 2. Differentiate it with respect to a:

dzda=2(a3)2aa2(a3)2=2a26a(a3)2

Put dzda=0

2a26a(a3)2=0

a26a=0

a=6

Step 3. At a=6, d2zda2= positive

when a=6 and b=4.

(ab)min=6×4=24

Hence, Option ‘B’ is Correct.


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