Suppose xy=−2 and dy/dt=−4. Find dx/dt when x=−1.

  -2

Step-by-step explanation:

Dividing the given equation by x, we find y to be ...

  y = -2/x

Then ...

  dy/dx = 2/x^2

and ...

  dy/dt = (2/x^2)dx/dt

  dx/dt = (x^2/2)dy/dt

When dy/dt = -4 and x=-1, this is ...

  dx/dt = (-1)^2/2(-4) = (1/2)(-4)

  dx/dt = -2

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).