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 idontknow February 9th, 2018 03:21 AM

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 ?

 Country Boy February 9th, 2018 04:47 AM

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.

 v8archie February 9th, 2018 05:28 AM

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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