My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 11th, 2012, 09:06 AM   #1
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

A moving point along a graph

A point is moving along the graph of y = 1/(1+x^(2)) such that dx/dt is 2 inches per second.

Find dy/dt for (a) x = -2, (b) x = 0, (c) x = 1 and (d) x = 3



If someone could show me how to set this problem up and solve for one of these above x's, I could take notes and to the rest.


Thanks!
mathkid is offline  
 
October 11th, 2012, 09:28 AM   #2
Global Moderator
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 11,801
Thanks: 262

Math Focus: The calculus
Re: A moving point along a graph

You want to use:



So, compute and use the given value of . Then plug in the given values for x.
MarkFL is offline  
October 11th, 2012, 11:13 AM   #3
Newbie
 
Joined: Oct 2012

Posts: 7
Thanks: 0

Re: A moving point along a graph

Go Parametrics!
Don't forget that reciprocals can be useful too!
simons545 is offline  
October 11th, 2012, 02:22 PM   #4
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

Mark

The implicit differentiation lingo is happening very slow for me.

I know first to take the derV. In doing so I get -2x/(1+x)^(2) = dy/dt but I don't know how to proceed from here
mathkid is offline  
October 11th, 2012, 03:07 PM   #5
Global Moderator
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 11,801
Thanks: 262

Math Focus: The calculus
Re: A moving point along a graph

Your expression for dy/dx isn't quite right. You want x to be squared within the parentheses.
MarkFL is offline  
October 11th, 2012, 03:19 PM   #6
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

Oh yes. OK I fixed that. Now what?
mathkid is offline  
October 11th, 2012, 03:23 PM   #7
Global Moderator
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 11,801
Thanks: 262

Math Focus: The calculus
Re: A moving point along a graph

Multiply both sides by dx/dt, then by the chain rule, the left side is dy/dt, which is what you want.

You are given values for x and dx/dt, so plug and chug.
MarkFL is offline  
October 11th, 2012, 03:32 PM   #8
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

Show me Mark. I will then frame it and hang it on my f-----! Wall as a master key
mathkid is offline  
October 11th, 2012, 03:38 PM   #9
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

At x =10 I'm getting...

-2x(DX/DT)/(1+x^(2)) ^(2)

= -2(10)(2)/(1+10^(2))^(2)

= -40/10201 inches per sec
mathkid is offline  
October 11th, 2012, 05:00 PM   #10
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

Is this right Mark?

dy/dx =(-2x DX/dt)/(1+x^(2))^(2)

for x = -2. 8/25 in per sec
for x = 0. 0 in/sec
for x = 6. -24/1369 in/sec
for x = 10. -40/10201 in/sec
mathkid is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
graph, moving, point



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Moving from a stable fixed point to a stable period 2 point Jacob0793 Real Analysis 4 March 13th, 2014 06:15 PM
A particle moving around a circle and a point mathkid Calculus 9 November 11th, 2012 07:26 PM
Plotting moving points in 2d graph FKeeL Algebra 0 September 10th, 2009 07:23 AM
test if a point will be in a moving cone Philipe Algebra 2 May 22nd, 2009 03:24 PM
Point on the Graph symmetry Algebra 1 June 14th, 2007 03:20 PM





Copyright © 2014 My Math Forum. All rights reserved.