Question

A bug is moving along the parabola y=x^2 at a rate such that its distance from the origin is increasing at a rate of 1 cm/min. At what rates are the x and y coordinates of the bug increasing when it is at the point (2,4)?

Answer 1

It is a related rates problem. I just don't know how to set up the problem

Answer 2

\[y = x^{2}\]
\[\frac{dy}{dt} = 2x \frac{dx}{dt}\]
letting "d" be distance
\[d^{2} =x^{2} +y^{2}\]
\[2d \frac{dd}{dt} = 2x \frac{dx}{dt} +2y \frac{dy}{dt}\]

Answer 3

Then do you just put in the point 2,4 for x and y to solve?

Answer 4

yes , find "d" distance to point (2,4) and sub in for dy/dt in distance equation

Answer 5

so it is squareroot of 6 then?

Answer 6

no

Answer 7

I'm confused then.

Answer 8

\[d = \sqrt{2^{2}+4^{2}} = \sqrt{20} = 2\sqrt{5}\]
dd/dt is given as 1
\[\rightarrow 2(2\sqrt{5}) = 2(2)\frac{dx}{dt}+2(4)[2(2) \frac{dx}{dt}]\]