Point on a Curve


by jgens
Tags: curve, point
jgens
jgens is offline
#1
Jan20-09, 10:27 PM
P: 1,623
1. The problem statement, all variables and given/known data

A particle moves along a path described by y = 4 - x^2. At what point along the curve are x and y changing at the same rate

2. Relevant equations

Simple equations regarding derivatives.

3. The attempt at a solution

It's been a while before I've done any related rates problems, could someone please let me know if this is correct:

Since, x and y must be changing at the same rate (presumably with respect to time) x' = y' and y' = -2xx'. Therefore, -2x = 1 and x = -1/2. Placing my x value into the original equation yields 15/4. Hence, the point is (-1/2, 15/4).

Thanks.
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
mrdoe
mrdoe is offline
#2
Jan20-09, 10:37 PM
P: 36
SEEMS correct...
Dick
Dick is offline
#3
Jan20-09, 11:08 PM
Sci Advisor
HW Helper
Thanks
P: 25,170
Of course, it's right. What could go wrong?

jgens
jgens is offline
#4
Jan20-09, 11:13 PM
P: 1,623

Point on a Curve


Plenty, I could have made an incorrect assumption ultimately leading to false conclusions.
quasar987
quasar987 is online now
#5
Jan20-09, 11:15 PM
Sci Advisor
HW Helper
PF Gold
quasar987's Avatar
P: 4,768
Good answer but you do not need to assume that x and y are varying wrt an external parameter. The derivative y'(x) = dy/dx of y wrt x expresses the instantaneous rate of change of y wrt a change in x.

The points where y and x are changing at the same rate are those where y'(x)=1.


Register to reply

Related Discussions
find an equation of the tangent line to the curve at the given point Calculus & Beyond Homework 23
Given a point and a curve: how to find perpindicular POI? Calculus 10
Find the slope of the tangent to the curve at the point where x = a Calculus & Beyond Homework 4
Point on a curve question Calculus & Beyond Homework 5
peak point of a curve General Math 13