Differential Equation

Question

The differential equation  .

I. produces a slope field with horizontal tangents at y = 4

II. produces a slope field with horizontal tangents at x = 0

III. produces a slope field with vertical tangents at x = 0 and y = 4

Question options:

1)	I only
2)	II only
3)	I and II
4)	III only

Answer 1

dy/dx = 2x(4 - y) = 0. So 2x(y - 4) = 0. And we have x = 0 or y = 4.

Answer is 4)

Answer 2

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

When y = 4, dy / dx = (2x) (4 - 4) = 0. A slope of zero will create a horizontal line.

When x = 0, dy / dx = (2*0) (4 - y) = 0. A slope of zero will create a horizontal line.

Options I and II are correct.