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 $\displaystyle xsinx = 0$ which equation i dont know to solve any request ? 
February 9th, 2018, 05:47 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 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.

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.


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