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Another polynomial function

  1. Oct 31, 2011 #1
    1. The problem statement, all variables and given/known data

    f:[1,+∞[→ℝ
    x→sqrt(x+2)-sqrt(x-1)


    2. Relevant equations

    show that f([1,+∞[)=]0,sqrt(3)]


    3. The attempt at a solution

    Any tips on how to start it.
     
    Last edited: Oct 31, 2011
  2. jcsd
  3. Oct 31, 2011 #2

    Ray Vickson

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    What have you done so far?

    RGV
     
  4. Oct 31, 2011 #3
    well nothing really, i want something that'll help me get going.
     
  5. Oct 31, 2011 #4

    Deveno

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    things to try:

    1. calculate f(x) explicitly for a few values of x. i always like 0,1,-1 and 42 (ok, 0,1 and-1 won't work. pick something else. maybe 2,4 and 6)

    2. see if lim x→∞ and lim x→1+ exist.

    3. see if f(x) has a global maximum or minimum (yeah, derivatives, we can use them, right?)
     
  6. Oct 31, 2011 #5
    alright so these 3 steps should help me?
     
  7. Oct 31, 2011 #6

    Deveno

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    you want to figure out how f(x) behaves. you need to get some information.
     
  8. Oct 31, 2011 #7
    yea but in class when we want to solve something like this he have to show that f(x)=y or f(x)≥0.
     
  9. Oct 31, 2011 #8

    Deveno

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    what is f(1)?

    we need to establish "some" things about f. it's going to be impossible to do, if all you think is "well, f is a function".

    take it's derivative. it is always positive, does it ever equal 0, is it some places positive, and some places negative? what does that tell you about f?

    are there any places where f(x) = 0 (does this have anything to do with whether or not f crosses the x-axis)?

    what happens when x gets "really really big"? does it have a limit as x→∞? if so, what is this limit?
     
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