What is the slope of the line tangent to the curve 3y² - 2x² = 6 - 2xy at the point (3, 2)?

Solution:

Given curve 3y² - 2x² = 6 - 2xy

Slope of the tangent line can be computed by differentiating the function/curve

Taking derivative on both sides , we get

6ydy - 4xdx = -2(xdy + ydx)

6ydy - 4xdx = -2xdy - 2ydx

6ydy + 2xdy = (4x - 2y) dx

dy/dx = (4x - 2y) / (6y + 2x)

f’(x, y) at (3, 2) = (4(3) - 2(2) )/ )6(2) + 2(3))

f’(x, y) = (12 - 4) / (12 + 6)

=8/18

f’(x, y)= 4/9

Hence, the slope of the tangent line is 4/9.

What is the slope of the line tangent to the curve 3y² - 2x² = 6 - 2xy at the point (3, 2)?

Summary:

The slope of the line tangent to the curve 3y² - 2x² = 6 - 2xy at the point (3, 2) is 4/9.