Question

Let f(x,y)=xy

(a) Find an equation for the tangent line to the level curve of f through the point (2,−2).

Answer 1

To find the equation of the tangent line to the level curve of f(x,y) = xy through the point (2,−2), we need to find its slope and the point of tangency.

Step-by-step explanation:

To find the equation of the tangent line to the level curve of f(x,y) = xy through the point (2,−2), we need to find its slope and the point of tangency.

Step 1: Find the partial derivatives of f(x, y) with respect to x and y.

Step 2: Evaluate the partial derivatives at the point (2,−2) to find the slope.

Step 3: Use the point-slope form of a line to find the equation of the tangent line using the slope and the given point.

Therefore, the equation of the tangent line is y = -4x - 10.