February 9th, 2018, 04:21 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 194 Thanks: 23  Extremum of y
Find extremum of $\displaystyle y=\cos x + \frac{x^2 }{2}$ using derivative i get $\displaystyle xsinx = 0$ which equation i dont know to solve any request ? 
February 9th, 2018, 05:47 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,948 Thanks: 797 
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.

February 9th, 2018, 06:28 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,143 Thanks: 2383 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.


Tags 
extremum 
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 