Finding roots, extrema, and concavity of f(x) = sin(x/2)

[d_leet]

I don't know why there is a 2 and a 4 at the end and a -1 in front...i know that sinx=cosx and that cosx=-sinx..?

NO!

It is absolutely not true that

sin(x) = cos(x) for all x.

or

cos(x) = -sin(x) for all x.

Do you understand what the problem is with what you wrote.

However it is true that the first derivative of sin(x) is equal to cos(x) and that the first derivative of cos(x) is equal to -sin(x).

 

[quantumdude]

I don't know why there is a 2 and a 4 at the end and a -1 in front...

I gave you the differentiation rules. Have you tried to use them? If so then present your work and we'll show you what's wrong with it.

i know that sinx=cosx and that cosx=-sinx..?

No. Put a derivative operator in front of the left side of each of those equations, and then they will become true.

 

[frenkie]

how do you find end behavior of the function sin(x/2)

 

[d_leet]

how do you find end behavior of the function sin(x/2)

What do you know about the function y = sin(x)?

Surely the behavior of y = sin(x/2) should be similar..

 

[frenkie]

end behavior is a straight line going to negative and positive infinity?

 

[d_leet]

end behavior is a straight line going to negative and positive infinity?

What are you talking about? What does the graph of the function y = sin(x) look like?

 

[frenkie]

its an even graph going up to 1 and down to -1...

 

[HallsofIvy]

No, it's not. Since your idea of solving math problems appears to be punching calculator keys, more or less at random, how about graphing sin(x) on a calculator and looking at it?

 

[arildno]

As a follow-up to Halls' suggestion, let Xmin=-20, Xmax=20, Ymin=-1, Ymax=1 (on the Window menu).

What does the graph tell you?

 

[frenkie]

it tells you that the roots of sin(x/2) are at -2Pi, o and 2Pi? this is HARD!

 

[d_leet]

it tells you that the roots of sin(x/2) are at -2Pi, o and 2Pi? this is HARD!

Yes... But there are a lot more zeros than that... What do you know about the sine function?

 

[frenkie]

well its an even function...limits at negative and positive infinity...root at zero? what do u mean when u say there are a lot more zeros?

 

[d_leet]

well its an even function...limits at negative and positive infinity...root at zero? what do u mean when u say there are a lot more zeros?

How can you be asking these questions when you are supposed to be finding the extrema of this function? Surely you must be in a calculus class, and in my experience most calculus classes require some prerequisite knowledge of trigonometry and trigonometric functions. You do realize that the sine funtion is a trigonometric fundtion right?

Next, What does it mean mathematically for a function to be even? Because f(x) = sin(x) is absolutely not an even function.

If a function is even it satisfies the following equlity.
f(x) = f(-x)
graphically this means that the function is symmetric about the y axis.

I have no clue what you mean by "limits at positive and negative infinity" because you give no context for them in the post I have quoted.

And when I say there are a lot more than three zeros, I specifically mean that there are an infinite number of zeros for the function y = sin(x/2) just as there are of the function y = sin(x). If you do not know this you are in no position to be speaking of the limits as x goes to positive or negative infinity, or finding the local extrema of this function. I suggest that you do a bit of research on the sine function before you make any more attempts at this problem.

 

[frenkie]

can u tell me what is greater then 2Pi on a unit circle? please. that's what i need to know.

 

[d_leet]

can u tell me what is greater then 2Pi on a unit circle? please. that's what i need to know.

What are you talking about?

 

[frenkie]

what is greater then 2Pi on a unit circle? it has nothing to do with this problem, i just need to know.

 

[frenkie]

what is greater then 2Pi on a unit circle? it has nothing to do with this problem i just need to know.

 

[d_leet]

what is greater then 2Pi on a unit circle? it has nothing to do with this problem, i just need to know.

It would really help if you would give some context as to what you are talking about, however I would suppose that 3pi, 4pi, 5pi, 1729pi etc.. would all be greater that 2pi...

 

[HallsofIvy]

You are trying to do Calculus problems when you cannot do basic algebra or even arthmetic. I strongly urge you to go to your teacher. You have far worse problems than we can help you with.