Question

If a curve passes through the point $(2,\frac{7}{2})$ and has slope $(1-\frac{1}{x^2})$ at any point $(x,y)$ on it, then the abscissa of the point on the curve whose ordinate is $\frac{-3}{2}$ is ____

• A. $2$
• B. $-2$
• C. $1$
• D. $-1$

Answer 1

The correct option is B $-2$

$\frac{dy}{dx}=1-\frac{1}{x^2}⟹\int dy=\int (1-\frac{1}{x^2})dx=x+\frac{1}{x}+c$

$(2,\frac{7}{2})$ lies on the curve $c=1$.

Curve $y=x+\frac{1}{x}+1⟹y=\frac{-3}{2}⟹x=-2,\frac{-1}{2}$