207k views
4 votes
Write a formula for the distance between a point (x, y) on the graph of y = x^4 and the point (1, 10). Express your answer in terms of x.

User Candi
by
8.3k points

1 Answer

4 votes
Anonymous's answer is completely correct. I thought this problem was asking how to find the distance along the function from the point (2,2^8), and wrote the answer to that nice, tasty problem.

Simply integrate the line element with respect to some affine parameter!

L=∫10(∂x∂λ)2+(∂y∂λ)2−−−−−−−−−−−−−L=∫01(∂x∂λ)2+(∂y∂λ)2

In this case,
x(λ)=λ(X−2)+2,x(λ)=λ(X−2)+2,
y(λ)=(λ(X−2)+2)8.y(λ)=(λ(X−2)+2)8.

Note that this approach can also solve the original problem, with some simplification.
User Paul Smith
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories