Find all extrema in the interval$\displaystyle [0,2{\pi}] $if y=x + sin x.

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- Jul 30th 2007, 04:00 AMSamanthaextremum
Find all extrema in the interval$\displaystyle [0,2{\pi}] $if y=x + sin x.

- Jul 30th 2007, 04:15 AMgalactus
First, find your derivative.

$\displaystyle f'(x)=1+cos(x)$

$\displaystyle 1+cos(x)=0$

What solutions to this fall in your interval?.

Here's a graph. They always help. - Jul 30th 2007, 04:46 AMSamantha
is it

a)$\displaystyle (-1,-1+ \frac {3\pi} {2}), (0,0)$

b) $\displaystyle (2 {\pi}, 2{\pi})$ (0,0)

c) $\displaystyle (2{\pi}, 2{\pi}), ({\pi},{\pi})$

d) $\displaystyle ({\pi},{\pi}), $(0,0)

e) None of these - Jul 30th 2007, 04:54 AMCaptainBlack
- Jul 30th 2007, 05:04 AMSamantha
- Jul 30th 2007, 05:07 AMgalactus
I'm sorry to say, you should see your professor if you're that lost.

- Jul 31st 2007, 11:40 AMSamantha
That's how I did it and understand it. Plz help

y=x+sinx

y(prime)=1+cosx

cosx=-1

x=$\displaystyle \pi$

so the answer it $\displaystyle (\pi, \pi)$ - Jul 31st 2007, 12:41 PMtopsquark
- Aug 1st 2007, 04:18 AMSamantha
- Aug 1st 2007, 04:31 AMtopsquark