Applications Of Derivatives Question 161
Question: The curve given by $ x+y=e^{xy} $ has a tangent parallel to the y-axis at the point
[AMU 2005]
Options:
A) (0, 1)
B) (1, 0)
C) (1, 1)
D) (-1, -1)
Show Answer
Answer:
Correct Answer: B
Solution:
Curve $ x+y=e^{xy} $ Differentiating with respect to x $ 1+\frac{dy}{dx}=e^{xy}( y+x\frac{dy}{dx} ) $ or $ \frac{dy}{dx}=\frac{ye^{xy}-1}{1-xe^{xy}} $
$ \frac{dy}{dx}=\infty \Rightarrow 1-xe^{xy}=0\Rightarrow 1-x(x+y)=0 $ This hold for $ x=1 $ , $ y=0 $ .
BETA
