Question

In the xy-plane, the line tangent to the graph of x² + xy + y = 3 at the point (1, 1) has a slope of​

Answer 1

Answer:

The slope of the tangent line is -3/2.

Step-by-step explanation:

The slope of a tangent line is given by the derivative evaluated at the point of tangency.

To find the derivative dy/dx, use implicit differentiation.

The derivative of the first term is 2x.

The derivative of the second term is found by using the Product Rule.

The derivative of  y  is dy/dx.

The derivative of 3 is 0.

Differentiating each term produces

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

Solve for dy/dx.

$2x+y+(x+1)\frac{dy}{dx}=0 \\\frac{dy}{dx}=\frac{-2x-y}{x+1}$

Plug in the point (1, 1).

$\frac{dy}{dx}=\frac{-2-1}{1+1} =-\frac{3}{2}$