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: 11,566
Thanks: 108

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
 
Joined: Oct 2012

Posts: 6
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: 11,566
Thanks: 108

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: 11,566
Thanks: 108

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  
October 11th, 2012, 06:46 PM   #11
Global Moderator
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 11,566
Thanks: 108

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

Yes, those numbers are right.

As a follow-up, can you find the point(s) at which dy/dt is changing the most rapidly?
MarkFL is offline  
October 11th, 2012, 06:50 PM   #12
 
Joined: Aug 2012
From: South Carolina

Posts: 866
Thanks: 0

Re: A moving point along a graph

Not sure. How?

Do I divide nim by den?
mathkid is offline  
October 11th, 2012, 07:17 PM   #13
Global Moderator
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 11,566
Thanks: 108

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

Hint: you want to find where:



Do you see why?

Hey, I know you are loaded down with homework, so only if you get done with your assigned work and you feel like fooling with this...
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
graph, moving, point


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.