Question

Find the point(s) on the parabola y=x^2 which is/are closest to the point (0,2). Fully justify your answer using calculus.

Answer 1

you want to minimize distance from parabola to point

using distance formula
\[d = \sqrt{(x-0)^2 + (y-2)^2} = \sqrt{x^2 + (x^2 -2)^2}\]
set derivative equal to 0
solve for x

Answer 2

I got the points (-sqrt{3/2},3/2) and (sqrt{3/2},3/2)

Would these be correct?

Answer 3

yes thats correct

Answer 4

Yay thank you!