My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree2Thanks
  • 1 Post By Country Boy
  • 1 Post By johng40
Reply
 
LinkBack Thread Tools Display Modes
April 14th, 2017, 08:25 PM   #1
Newbie
 
Joined: Nov 2016
From: USA

Posts: 16
Thanks: 1

Please clarify the final step of this proof (inflection point)

Here is the solution to proving the inflection point of y=xsinx lies on the curve y^2(x^2+4)=4x^2

y''
2cosx - xsinx = 0
xsinx=2cosx

(hereafter all are x's are x sub zero)
inflection point of the curve (x, 2cos x)
Prove (x,2cosx) lies on the curve y^2(x^2+4)=4x^2

(2cosx)^2(x^2+4)=4x^2
4cos^2x[(4 cos^2x/sin^2x) +4] = 4[(2cosx)/sinx]^2
16 (cos^2x/sin^2x) = 16 (cos^2x/sin^2x)

How does the first bolded equation equal the second bolded equation?
Seventy7 is offline  
 
April 15th, 2017, 05:05 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,340
Thanks: 588

4cos^2(x)/sin^2(x)+ 4= 4((cos^2(x)/sin^2(x))+ 1)= 4(cos^2(x)sin^2(x)+ sin^2(x)/sin^2(x))= 4((cos^2(x)+ sin^2(x))/sin^2(x))= 4/sin^2(x).

Multiplying that by 4 cos^2(x) gives 16 cos^2(x)/sin^2(x).
Thanks from Seventy7
Country Boy is offline  
April 15th, 2017, 06:57 AM   #3
Member
 
Joined: Jan 2016
From: Athens, OH

Posts: 30
Thanks: 16

First comment: I don't like the way you started the proof.
Quote:
(2cosx)^2(x^2+4)=4x^2
This is really starting with what you want to prove. You should start with the left side of the equation and derive the right side as follows:



The following graphs show the result and also the fact that there are infinitely many inflection points. But also notice not every intersection of the two graphs is an inflection point.

Thanks from Seventy7
johng40 is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
clarify, final, inflection, point, proof, step



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
how did they come to the final step of this equation? vlekje5 Pre-Calculus 3 April 12th, 2017 11:32 AM
A point of inflection is a turning point or not helloprajna Calculus 5 February 6th, 2015 03:57 AM
Inflection point paper006 Calculus 1 June 2nd, 2014 11:31 AM
Point of Inflection JenniferC Calculus 2 January 23rd, 2014 05:12 PM
Inflection point ungeheuer Calculus 2 August 21st, 2013 02:29 PM





Copyright © 2017 My Math Forum. All rights reserved.