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 February 9th, 2018, 04:21 AM #1 Senior Member   Joined: Dec 2015 From: iPhone Posts: 385 Thanks: 61 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 ?
 February 9th, 2018, 05:47 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 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: 7,599 Thanks: 2587 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

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