A point moves along the curve y=(x-2)^2 such that the x coordinate is increasing at 2 units per second. At the moment x=1, how fast is its y coordinate changing.

Answer 1

y = (x-2)^2
y = x^2-4x -4
dy = 2xdx - 4dx
so,
dy/dx = 2x-4
dx/dt = 2
so,
dy/dt = dy/dx dx/dt
= 2(2x-4)
= 4x-8
for x=1 then
dy/dt = 4(1)-8 = -4 units per second