Question

Problem set 1 1c-5, how is the tangent line through (a, 1+(a-1)^2) going to be y = 2(a-1)(x-a)+1+(a-1)^2 ?

Answer 1

I believe this is just point slope form.. \[y-y _{0}=m(x-x _{0}) \]\[y=m(x-x_{0})+y_{0}\]To get 'm' you just take the derivative..\[m = d/dx[1+(a-1)^{2}] = 2(a-1)\]\[(x_{0}, y _{0}) = (a, 1+(a-1)^{2})\]\[y=2(a-1)(x-a)+(1+(a-1)^{2})\]Hopefully, this answers your question!

Answer 2

I see it now, thank you!