1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need Help asap!

  1. Mar 24, 2006 #1
    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.
    please help..any help is greatly appreciated.
     
  2. jcsd
  3. Mar 24, 2006 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Need: Show your own work first.
     
  4. Mar 24, 2006 #3
    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?
     
  5. Mar 24, 2006 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    There will be an infinite number of roots. What is the interval you are required to solve for?
     
  6. Mar 24, 2006 #5

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You are using TEXAS, right?

    Are you absolutely sure you were asked to do this by aid of a calculator?
     
  7. Mar 24, 2006 #6
    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.;-(
     
  8. Mar 24, 2006 #7

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, let's take the roots first:
    Letting y=x/2, when is sin(y)=0?
     
  9. Mar 24, 2006 #8
    when x=0, is that the only root? or is there more?
     
  10. Mar 24, 2006 #9

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Think about a sin function. Where does it cross the x-axis?
     
  11. Mar 24, 2006 #10
    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?
     
  12. Mar 24, 2006 #11

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    Now you need to think about your function [itex]f(x) = \sin\left( \frac{x}{2} \right)[/itex], where will the crossing points be?
     
  13. Mar 24, 2006 #12
    i believe they will be at 0, negative pie and 2pie. since one cycle i pie. and there are 2 complete cycles.
     
  14. Mar 24, 2006 #13

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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).
     
  15. Mar 24, 2006 #14
    plug in Pi for x in the original equation? :-(
     
  16. Mar 24, 2006 #15
    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.
     
  17. Mar 24, 2006 #16

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well:
    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?
     
  18. Mar 24, 2006 #17
    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.
     
  19. Mar 24, 2006 #18
    First and second derivative tests maybe...
     
  20. Mar 24, 2006 #19
    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.
     
  21. Mar 24, 2006 #20
    The first derivative of that function certainly has more than 1 zero, and x=0 is definitely not one of them.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Need Help asap!
  1. D3y/dx3 OF Y= 1/X+1 (Replies: 1)

Loading...