# Homework Help: Need Help asap!

1. Mar 24, 2006

### frenkie

original equation: f(x)=sin(x/2)
need: show work on how to find roots, POI, min, max.
intervals of increase/descrease.
intervals of concavity, end behavior.

2. Mar 24, 2006

### arildno

Need: Show your own work first.

3. Mar 24, 2006

### frenkie

to find a root i plugged the equation into the calculator in the y= and i graphed it and pushed 2nd trace and pushed #2, and then it asked me to pick a number less then o and greater then o so I picked -2 and 2 and it gave me a root at x=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. Mar 24, 2006

### Hootenanny

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

5. Mar 24, 2006

### arildno

You are using TEXAS, right?

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

6. Mar 24, 2006

### frenkie

need to do it by hand...i know that to find the root i need to set the original equation to 0 and solve, but i'm stuck because i never did it with trig functions. i also konw that to find mins and maxs you are suppose to set the second derivative = to 0, but again, stuck.

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

7. Mar 24, 2006

### arildno

Well, let's take the roots first:
Letting y=x/2, when is sin(y)=0?

8. Mar 24, 2006

### frenkie

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

9. Mar 24, 2006

### Hootenanny

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

10. Mar 24, 2006

### frenkie

from the interval of -10 to 10 sin function crosses the x-axis at 3, 6, 9 same for the negative. and sin(x/2) crosses at -6,0,6...so these are the 3 roots of the equation from -10 to 10?

11. Mar 24, 2006

### Hootenanny

Staff Emeritus
I assume your working in radians.Your answers are correct, however it is more usual to give them in terms of $\pi$, for example, $\pi , 2\pi , 3\pi$ etc.

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

12. Mar 24, 2006

### frenkie

i believe they will be at 0, negative pie and 2pie. since one cycle i pie. and there are 2 complete cycles.

13. Mar 24, 2006

### arildno

So, can you find some GENERAL formula for the zeroes out of this?
(Hint: It has something to do with multiples of a famous number).

14. Mar 24, 2006

### frenkie

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

15. Mar 24, 2006

### d_leet

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. Mar 24, 2006

### arildno

Well:
What do you think the following expressions equals:
$$\sin(-3\pi), \sin(4\pi), \sin(7\pi)$$

What is the common feature with these expressions?

17. Mar 24, 2006

### frenkie

yeah true..I don't konw what the equation is...anybody know how to find POI of the equation and min/max? i know how to find it on the graph but I don't know how to do it and show work.

18. Mar 24, 2006

### d_leet

First and second derivative tests maybe...

19. Mar 24, 2006

### frenkie

you mean set the first derivative equal to 0? and then the numbers you get you plug into the original equation? because when i set the first derivative equal to 0 i get x=0 as my only answer.

20. Mar 24, 2006

### d_leet

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