- #1

frenkie

- 37

- 0

need: show work on how to find roots, POI, min, max.

intervals of increase/descrease.

intervals of concavity, end behavior.

please help..any help is greatly appreciated.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter frenkie
- Start date

- #1

frenkie

- 37

- 0

need: show work on how to find roots, POI, min, max.

intervals of increase/descrease.

intervals of concavity, end behavior.

please help..any help is greatly appreciated.

- #2

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

Need: Show your own work first.

- #3

frenkie

- 37

- 0

for the POI, i graphed it and looked at where the concavity changes. (not sure if its correct)

for limits i just looked at the graph and saw that as x goes to infinity y goes to 1 and as x goes to negative infinity y goes to -1.

and for the mins and max's i also looked at the graph and everytime thre was a concave up i put a min and everytimet here was a concave down i put a max. right?

- #4

Hootenanny

Staff Emeritus

Science Advisor

Gold Member

- 9,624

- 8

There will be an infinite number of roots. What is the interval you are required to solve for?

- #5

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

Are you absolutely sure you were asked to do this by aid of a calculator?

- #6

frenkie

- 37

- 0

and the intervals are -infinity to infinity.;-(

- #7

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

Well, let's take the roots first:

Letting y=x/2, when is sin(y)=0?

Letting y=x/2, when is sin(y)=0?

- #8

frenkie

- 37

- 0

when x=0, is that the only root? or is there more?

- #9

Hootenanny

Staff Emeritus

Science Advisor

Gold Member

- 9,624

- 8

frenkie said:when x=0, is that the only root? or is there more?

Think about a sin function. Where does it cross the x-axis?

- #10

frenkie

- 37

- 0

- #11

Hootenanny

Staff Emeritus

Science Advisor

Gold Member

- 9,624

- 8

Now you need to think about your function [itex]f(x) = \sin\left( \frac{x}{2} \right)[/itex], where will the crossing points be?

- #12

frenkie

- 37

- 0

- #13

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

So, can you find some GENERAL formula for the zeroes out of this?frenkie said:

(Hint: It has something to do with multiples of a famous number).

- #14

frenkie

- 37

- 0

plug in Pi for x in the original equation? :-(

- #15

d_leet

- 1,077

- 1

frenkie said:plug in Pi for x in the original equation? :-(

But if the original equation is y = sin(x/2) then letting x = pi you get

y = sin(pi/2) = 1 So that certainly isn't a zero.

- #16

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,089

- 135

What do you think the following expressions equals:

[tex]\sin(-3\pi), \sin(4\pi), \sin(7\pi)[/tex]

What is the common feature with these expressions?

- #17

frenkie

- 37

- 0

- #18

d_leet

- 1,077

- 1

frenkie said:

First and second derivative tests maybe...

- #19

frenkie

- 37

- 0

- #20

d_leet

- 1,077

- 1

frenkie said:

The first derivative of that function certainly has more than 1 zero, and x=0 is definitely not one of them.

- #21

frenkie

- 37

- 0

derivative of sin(x/2) is cos(x/2)? and the second derivative is -sin(x/2)?

- #22

d_leet

- 1,077

- 1

frenkie said:derivative of sin(x/2) is cos(x/2)? and the second derivative is -sin(x/2)?

Close, but you need to remember the chain rule.

- #23

frenkie

- 37

- 0

what is the derivative of (x/2)?

- #24

frenkie

- 37

- 0

- #25

d_leet

- 1,077

- 1

frenkie said:

How are you not sure how you got it? And oddly enough your second derivative is correct but the first derivative you found is wrong..

- #26

matt grime

Science Advisor

Homework Helper

- 9,426

- 4

This isn't me saying 'gosh, how can someone not know *that*' but asking 'how can someone who doesn't know that be in a class that asks them to find the points of inflexion of sin(x/2)'?

- #27

frenkie

- 37

- 0

- #28

quantumdude

Staff Emeritus

Science Advisor

Gold Member

- 5,575

- 23

Here are two hints:

If [itex]u[/itex] is a differentiable function of [itex]x[/itex] then we have:

[tex]\frac{d}{dx}\sin(u)=\cos(u)u'[/tex]

[tex]\frac{d}{dx}\cos(u)=-\sin(u)u'[/tex]

As for the derivative of [itex]\frac{x}{2}[/itex] simply recall that [itex]\frac{x}{2}=\frac{1}{2}x[/itex] and use the appropriate differentiation rule.

- #29

matt grime

Science Advisor

Homework Helper

- 9,426

- 4

- #30

frenkie

- 37

- 0

- #31

d_leet

- 1,077

- 1

frenkie said:

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

- #32

quantumdude

Staff Emeritus

Science Advisor

Gold Member

- 5,575

- 23

frenkie said: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

- #33

frenkie

- 37

- 0

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

- #34

d_leet

- 1,077

- 1

frenkie said: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..

- #35

frenkie

- 37

- 0

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

Share:

- Last Post

- Replies
- 1

- Views
- 2K

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 12

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 32K

- Last Post

- Replies
- 3

- Views
- 2K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 3K

- Last Post

- Replies
- 8

- Views
- 31K

- Replies
- 6

- Views
- 625