Question

The curve given by $x+y=e^{xy}$ has an tangents parallel to the y-axis at the point

• A. $(0,1)$
• B. $(1,0)$
• C. $(1,1)$
• D. $(0,0)$

Answer 1

The correct option is B $(1,0)$

$\frac{dy}{dx}$(differentiate the terms)

$1+\frac{dy}{dx}=e^{xy}(x\frac{dy}{dx}+y)$

$\Rightarrow \frac{dy}{dx}=\frac{y{e}^{xy}-1}{1-x{e}^{xy}}$

Check by option

$\frac{dy}{dx}|{}_{(0,1)}=\frac{1-1}{1-0}=\frac{0}{1}=0$ Not coming infinity

$\frac{dy}{dx}|{}_{(1,0)}=\frac{-1}{0}=\infty$

This point satisfy

$\therefore$ option B$(1,0)$.