My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

Thanks Tree1Thanks
  • 1 Post By v8archie
LinkBack Thread Tools Display Modes
February 9th, 2018, 04:21 AM   #1
Senior Member
Joined: Dec 2015
From: Earth

Posts: 262
Thanks: 29

Extremum of y

Find extremum of $\displaystyle y=\cos x + \frac{x^2 }{2}$
using derivative i get $\displaystyle x-sinx = 0$
which equation i dont know to solve
any request ?
idontknow is offline  
February 9th, 2018, 05:47 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

An obvious solution is x= 0 and, in fact, looking at graphs of y= sin(x) and y= x, it is clear that is the only solution.
Country Boy is offline  
February 9th, 2018, 06:28 AM   #3
Math Team
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
As Country Boy says, $x=0$ is an obvious solution. Solutions come at the zeros of $f(x)=x-\sin x$ (this much should be obvious). Now $f'(x) = 1 - \cos x$ and so $f'(x) \ge 0$ for all $x$. This should allow you to prove that there are no solutions other than the one that you have already found.
Thanks from Country Boy
v8archie is offline  

  My Math Forum > College Math Forum > Calculus


Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Extremum values idontknow Calculus 3 April 22nd, 2017 02:05 PM
Derivative at extremum jkh1919 Calculus 3 July 24th, 2012 07:49 PM
derivative of extremum anigeo Calculus 2 May 12th, 2012 07:50 AM
Extremum search thescratchy Calculus 6 March 5th, 2011 07:41 PM
Extremum StevenMx Calculus 3 December 16th, 2008 11:13 AM

Copyright © 2018 My Math Forum. All rights reserved.