My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

Thanks Tree3Thanks
  • 1 Post By Pero
  • 1 Post By MarkFL
  • 1 Post By 21joanna12
LinkBack Thread Tools Display Modes
August 21st, 2014, 01:15 PM   #1
Joined: Aug 2014
From: England

Posts: 2
Thanks: 1

Determining the nature of a stationary point?


I think I must be losing my mind because I cannot figure out a perfectly simple problem. I am supposed to find the coordinates of, and determine the nature of, the stationary point(s) of the curve:


So differentiating it you get

dy/dx = 12(2x-3)^5

So there is a single stationary point at (1.5,0)

and differentiating it again you get

d^2y/dx^2 = 120(2x-3)^4

So at x=1.5 you get that the second derivative is equal to zero, so that means it's a point of inflexion, right? But it is actually a minimum point...

Would be very grateful if someone could point out where I am going wrong!

Thanks in advance
21joanna12 is offline  
August 21st, 2014, 01:23 PM   #2
Senior Member
Joined: Jun 2013
From: London, England

Posts: 1,316
Thanks: 116

What about $\displaystyle y = x^4$?
Thanks from 21joanna12
Pero is offline  
August 21st, 2014, 01:25 PM   #3
Senior Member
MarkFL's Avatar
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,209
Thanks: 517

Math Focus: Calculus/ODEs
The second derivative being equal to zero is only one requirement for an inflection point. The other is that the sign of the second derivative must change across that point. Is this the case here?
Thanks from 21joanna12
MarkFL is offline  
August 22nd, 2014, 12:41 AM   #4
Joined: Aug 2014
From: England

Posts: 2
Thanks: 1

I see...

So I guess whenever you get a second derivative of zero you have to check what it means by seeing what is going on on either side...

Thank you
Thanks from MarkFL
21joanna12 is offline  

  My Math Forum > College Math Forum > Calculus

determining, nature, point, stationary

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Maths in nature. Rishabh Math 1 June 3rd, 2014 06:36 AM
Strict sense stationary and wide sense stationary grfadaei Advanced Statistics 0 January 21st, 2014 09:28 PM
Finding stationary point in Gaussian Mixture JohnDejong Algebra 0 December 10th, 2012 08:20 AM
Nature of stationary points yeoky Calculus 4 March 27th, 2010 11:29 PM
The Nature of Infinity roadnottaken Applied Math 44 January 22nd, 2007 08:18 PM

Copyright © 2019 My Math Forum. All rights reserved.