I need some help with this problem.

Find the points on the ellipse 4x^2 + y^2 = 4 that are farthest away from the point (1, 0).

d = sqrt[(x -1)^2 + (y - 0)^2]

4x^2 + y^2 = 1

=> x^2 + y^2/4 = 1

=> x^2 = 1 - y^2/4

=> x = sqrt(1 - y^2/4)

=> x = 1 - y/2 = -y

d = sqrt[(-y -1)^2 + (y - 0)^2]

d^2 = f(y) = (-y -1)^2 + (y -0)^2

f'(y) = 2(-y -1) + 2(y - 0) = -2y -2 + 2y - 0 = -2

I don't know what to do next, and I'm sure I've made a couple of mistakes anyway.

Thanks.