Question

If slope of tangent of curve $y=\frac{x}{b-x}$ at $(1,1)$ be $2$ then $b=$

• A. $1$
• B. $2$
• C. $0$
• D. $-1$
• E. $-2$

Answer 1

The correct option is B $2$

Given,

$y=\frac{x}{b-x}$

Now,

$\frac{dy}{dx}=\frac{(b-x)1+x.(-1)}{(b-x{)}^2}$

or, $\frac{dy}{dx}=\frac{b}{(b-x{)}^2}$.

Now,

${\frac{dy}{dx}|}_{(1,1)}=\frac{b}{(b-1{)}^2}$.

According to the problem,

$\frac{b}{(b-1{)}^2}=2$

or, $b=2(b^2-2b+1)$
or, $2b^2-5b+2=0$

or, $(2b-1)(b-2)=0$

or, $b=\frac{1}{2},2$.