If the slope of the curve `y=(ax)/(b-x)` at the point (1, 1) is 2, then find a & b

Options

A. `a=1, b= -2`
B. `a= -1,b=2`
C. `a=1,b=2`
D. none of these

Answer

C

Explanation

We have,
`y=(ax)/(b-x)rArr(dy)/(dx)=((b-x)a+ax)/((b-x)^(2))=(dy)/(dx)=(ab)/((b-x)^(2)) " ..(i)" `
`((dy)/(dx))_((1","1))=(ab)/((b-1)^(2))rArr (ab)/((b-1)^(2))=2" ...(ii)" `
Since, (1, 1) lies on (i). Therefore,
`1=(a)/(b-1) " ...(iii)" `
From (ii) and (iii), we have
`(b)/(b-1)=2rArr b=2`
Putting b = 2 in (iii), we get a = 1.
Hence, a = 1 and b =2.