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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.

  • Calculus -

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

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