Optimal Coordinates on y=x^4 Curve Using Newton's Method

[wildcat12]

Homework Statement

Find, correct to 6 decimal places, the coordinates of the points on the curve y=x^4 that are closest to the point (0,1)

Homework Equations

The Attempt at a Solution

I am not sure if i am supposed to use Newtons method or not

 

[micromass]

Take an arbitrary point on the curve y=x^4. This has the form (x,x^4). What is the distance between this point and (0,1)??
You'll need to minimize this distance (or rather its square, to keep the calculations manageable).

 

[vela]

Newton's method will certainly work. Give it a try.