Question

The curve $y-e^{xy}+x=0$ has a vertical tangent at the point

• A. (1,1)
• B. No point
• C. (0,1)
• D. (1,0)

Answer 1

The correct option is D

(1,0)

$\frac{dy}{dx}=-\frac{f_x}{f_y}=\infty =\frac{y{e}^{xy}-1}{1-x{e}^{xy}}\therefore 1-x{e}^{xy}=0\therefore e^{xy}=\frac{1}{x}.Also{e}^{xy}=x+y\therefore x+y=\frac{1}{x}$
This relation is statisfied by (1,0) only.