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x+y-ln(x+y)=2x+5 has a vertical tangent ...

`x+y-ln(x+y)=2x+5` has a vertical tangent at the point `(alpha,beta)` then `alpha+beta` is equal to

A

`-1`

B

`1`

C

`2`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Give `x + y - ln (x+y) = 2x + 5`
`rArr 1+ (dy)/(dx) - (1)/(x+y) (1+(dy)/(dx)) = 2`
`rArr (dy)/(dx) = (x+y+1)/(x+y-1)`
`(dy)/(dx)|_(alpha,beta) = (alpha+beta+1)/(alpha+beta-1) = oo` when `alpha+ beta = 1`
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