Home
Class 12
MATHS
If ab=2a+3b, agt0, b gt0, then the minim...

If `ab=2a+3b, agt0, b gt0`, then the minimum value of ab is

A

12

B

24

C

`(1)/(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`ab=2a+3b rArr b=(2a)/(a-3)`
Now `z=ab=(2a^(2))/(a-3)`
`rArr" "(dz)/(da)=(2[(a-3)2a-a^(2)])/((a-3)^(2))=(2[a^(2)-6a])/((a-3)^(2))`
Put `(dz)/(da)=0, therefore a^(2)-6a=0, a=0,6`
Clearly a = 6 is point of minima
when `a=6, b=4 rArr (ab)_("min")=6xx4=24`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|10 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension Type|2 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

Similar Questions

Explore conceptually related problems

If ab = 2a +3b, a gt0, b gt 0, then the minimum value of ab is-

If ab^2c^3,a^2b^3c^4,a^3b^4c^5 are in AP (a,b,cgt0) thgen the minimum value of a+b+c is

If abs(z-i)le2 and z_0=5+3i then the maximum value of abs(absiz+z_0) is

If gt0,ygt0 " and " xy=25 , then find the minimum value of x+y .

Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0 . Then the minimum value of ("det.(A)")/(b) is

If iz^3+z^2-z+i=0 then the value of abs(z) is

If Agt0,Bgtgt0andA+B=(pi)/(3) , find the maximum value of tan A tan B .

A straight line passing through the point (a,b) [where agt0and bgt0 ] intersects positive coordnate axes at the points p and Q respectively . Show that the minimum value of (OP+OQ) is (sqrta+sqrtb)^(2) .

If log_(a)b=2, log_(b)c=2, and log_(3) c= 3 + log_(3) a,then the value of c/(ab)is ________.