Newtons method?

wildcat12

1. The problem statement, all variables and given/known data
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)


2. Relevant equations



3. 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.