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## Homework Statement

Find the co-ordinates of all points on the curve f(x)= x

^{3}whose tangent lines pass through the point (a,0)

## Homework Equations

f '(x) = nx

^{n-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) = 3x

^{2}

y = 3x

^{2}(x-a)