1. The problem statement, all variables and given/known data Given that the curve y = x^3 has a tangent line that passes through point (0, 2), find the area of the region enclosed by the curve and the line by the following steps. 2. Relevant equations 3. The attempt at a solution Let f(x) = x^3 and let the coordinates of the point of tangency be (t, t^3) f'(x) = 3x^2, f'(t) = 3t^2 The equation of the tangent line is: y = 3t^2(x-t)+t^3 = 3t^2x - 2t^3 I am having trouble understand this part of the process. Particularly this step, y = 3t^2(x-t) + t^3. I have no idea what is happening at this step. Everything else I am completely aware of what is happening. If someone could help that would be great. Thanks!