Finding relative extrema and inflection points of f(x) = x/2 - sin(x) on (0, 2π)

[Cod]

For the function below, I have to find the exact values of x for which relative extreme exist and the exact values of x for which points of inflection exist.

$$f(x) = 1x/2 - sin(x)$$ when x is in the interval $$(0,2pi)$$

Here's what I have:

$$f'x = 1/2 - cos(x) = 0$$ (I'm not sure how to solve for x in this spot)

Also, for the finding the inflection points, I have this:

$$f"x = sin(x) = 0$$

$$x = 0/sin = 0$$ (This right? Or did I screw up before this?)



I guess my troubles are based around the basic trig functions as well as algebra. I'm in the process of moving, so my algebra book will be hard to find; however, I'm about to start looking.

Any help to point me in the right direction would be fantastic. Thanks.

 

[ShawnD]

First of all, wtf is up with your post? It there's a big black area and I can see some of the page's source code.

$$f'(x) = \frac{1}{2} -cos(x) = 0$$

$$cos(x) = \frac{1}{2}$$

You can either cheap out and use your calculator or you can draw those goofy triangles. http://myfiles.dyndns.org/math/value_triangle1.jpg is the one that applies in this case.
Turn 60 degrees into radians by dividing by 180 then multiplying by pi.

$$x = \frac{\pi}{3}$$


I can't even read what you have for inflection stuff because of the black area I mentioned.

$$f''(x) = sin(x) = 0$$

$$x = 0, \pi , 2\pi$$

That is NOT the answer though! The interval is between 0 and 2$$\pi$$ but those are rounded brackets. Round brackets mean you do NOT include the limits, that means 0 and 2$$\pi$$ are not answers.

$$x = \pi$$

 

[outandbeyond2004]

I have a program that finds roots. First extremum x is a little more than 1 radian and second about 5.20

 

[ShawnD]

Originally posted by outandbeyond2004
I have a program that finds roots. First extremum x is a little more than 1 radian and second about 5.20

Excellent point.

cos(x) = 1/2 is a referance angle. The first correct answer is pi/3. The second answer is mirrored around the x-axis (sine is mirrored around the y axis). The second answer should be 2pi - pi/3 which is 5pi/3 (about 5.23 as beyond had said).

 

[Cod]

Thanks for the help fellas. I don't know why my post looks like that. I checked it about 20 times looking for a mistake in the Latex coding, but there aren't any.