#1: The tangent at a point P on the curve y = x^3 intersects the curve again at a point Q. Show that the slope of the tangent at Q is four times the slope of the tangent at P. So far, I found the derivative of y = x^3, which is y' = 3x^2. Now I set these two equal to each other: X^3 = 3x^2 x^3 - 3x^2 = 0 x^2 (x-3) = 0 so x = 0 or x = 3. I don't know where to go from here, or if I did this right at all. #2: Show that the x- and y- intercepts for any tangent to the curve y = 16 - 8sqrt(x) + x have a sum of 16. First I expanded the equation: y = 16 - 8sqrt(x) + x = 16 - 8^(1/2) + x Then I determined the derivative: y' = -4x^(-1/2) + 1 = -4/sqrt(x) + 1 Once again, I have no idea what do from here. :( Any help would be greatly appreciated.