I have worked on this one for a while and I can not make my answer match the author's.
Find the points on the ellipse $4x^2 + y^2 = 4$ that are the farthest away from the point (1,0).
I have:
$$4x^2 + y^2 = 4$$
and then the distance formula, so I set y to terms of x and I get
$$\sqrt{(x-1)^2 + (2-2x)^2}$$
Setting the difference the a square this gives me a derivative of
$$10x-10$$
which gives me a zero of 1, this is wrong according to the book and I am not sure why.