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# Stationary points. Help? watch

1. Hi all,

I'm doing my maths homework and I'm stuck on a question. Might be quite simple but I just don't know where to go from here.

Q: Find the location of the stationary points of the function y = x + sinx in the interval 0 ≤ x < 2π.

I've differentiated it once, getting dy/dx = 1 + cosx.
I know that at any stationary point dy/dx = 0.
But how can I find the value of x?
2. (Original post by rachelweasley)
Hi all,

I'm doing my maths homework and I'm stuck on a question. Might be quite simple but I just don't know where to go from here.

Q: Find the location of the stationary points of the function y = x + sinx in the interval 0 ≤ x < 2π.

I've differentiated it once, getting dy/dx = 1 + cosx.
I know that at any stationary point dy/dx = 0.
But how can I find the value of x?
You need to make dy/dx = 0, so 1 + cosx = 0.

Rearrange this to make cosx = -1, and solve for x.

Just a question, is it just one stationary point you're looking for? There's only one solution in the range you've given and the question specifies stationary points.
3. (Original post by Craig1998)
You need to make dy/dx = 0, so 1 + cosx = 0.

Rearrange this to make cosx = -1, and solve for x.

Just a question, is it just one stationary point you're looking for? There's only one solution in the range you've given and the question specifies stationary points.
Thanks! Makes sense.

The question mentions stationary points (turning points and/or points of inflection). But if there's only one solution then perhaps I can only solve for one stationary point.
4. (Original post by rachelweasley)
Thanks! Makes sense.

The question mentions stationary points (turning points and/or points of inflection). But if there's only one solution then perhaps I can only solve for one stationary point.
If it's plural it means more than one, may have been an error. Do you have the answer given with you or not?
5. (Original post by Craig1998)
If it's plural it means more than one, may have been an error. Do you have the answer given with you or not?
Unfortunately, I don't. We're only given the answers after submitting the homework.
6. (Original post by rachelweasley)
Unfortunately, I don't. We're only given the answers after submitting the homework.
I'd stick with the single answer of (pi, pi). In an actual exam, they would never ask you to find stationary points if there was just 1, otherwise, consider the range given and make sure you have differentiated it right.

Also, if you are ever unsure of an answer, consider using wolframalpha. It's an extremely useful tool online which is free for the stuff you'll need it for. It will graph your equation and then suggest things like stationary points.

If you ask your teacher too, they may suggest other graphing software which your college/sixth form may have installed. For example, my college has Autograph, which graphs equations in a similar way to wolframalpha.

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