Find the co-ordinates of all points on the curve f(x)= x3 whose tangent lines pass through the point (a,0)
f '(x) = nxn-1
The Attempt at a Solution
I am really not sure how to attack this question. My initial thoughts are to find f '(x) then, given the points (a,0), create a point-slope equation for a line. But, this would only give me one equation. On the other hand, when I look at the graph of x^3 I can't see how two tangent lines could share a point. I'm not sure how I would find the co-ordinates either.
f '(x) = 3x2
y = 3x2 (x-a)