Question

If x² + xy – 3y = 3, then at the point (2, 1), dy/dx

Answer 1

Answer:

A

Step-by-step explanation:

We have the equation:

$x^2+xy-3y=3$

Take the derivative of both sides with respect to x:

$\frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3]$

Implicitly differentiate:

$2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0$

Solve for dy/dx:

$\frac{dy}{dx}(x-3)=-2x-y$

Divide:

$\frac{dy}{dx}=-\frac{2x+y}{x-3}$

To find dy/dx at (2, 1), substitute 2 for x and 1 for y. So:

$\frac{dy}{dx}_{(2, 1)}=-\frac{2(2)+1}{2-3}=-\frac{5}{-1}=5$

Hence, our answer is A.