Question

For the curve $\sqrt{x}+\sqrt{y}=1,\frac{dy}{dx}$ at $(1/4,1/4)$ is

• A. $1/2$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (C)

$-1$

We have,

$\sqrt{x}+\sqrt{y}=1$

On differentiating this with respect to x and we get,

$\frac{1}{2\sqrt{x}}+\frac{1}{2\sqrt{y}}\frac{dy}{dx}=0$

$\Rightarrow \frac{dy}{dx}=-\frac{\sqrt{x}}{\sqrt{y}}$

At the point $(\frac{1}{4},\frac{1}{4})$

So,

$\frac{dy}{dx}=-\frac{\sqrt{\frac{1}{4}}}{\sqrt{\frac{1}{4}}}$

$\frac{dy}{dx}=-1$

Hence, this is the answer.