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Rate of change from 1 to 2 for f(x)=2x^3 + x

  1. Apr 8, 2006 #1
    Find the average rate of change from 1 to 2 for the function f(x)=2x^3 + x

    so I did this:
    [f(2) – f(1)] – [2x^3 + x] / 2-1

    = 2-1-2x^3 + x / 1

    = 1-2x^3 + x

    = -2x^3 + x

    Right?
     
  2. jcsd
  3. Apr 8, 2006 #2

    Galileo

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    The average rate of change of f from a to b is
    [f(b)-f(a)]/(b-a)

    and it's (naturally) just a number. It doesn't depend on x. Check your definition.
     
  4. Apr 8, 2006 #3
    [2(2)^3 - 2(1)^3] - [2x^3 + x] / 2-1

    16-1-2x^3 + x / 1

    15-2x^3 + x

    I don't understand what you are telling me
     
  5. Apr 8, 2006 #4

    Galileo

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    You've got the definition of the average rate of change wrong.
    You wrote something like (f(2)-f(1)-f(x))/(2-1).
    By definition, the average rate of change of f on the interval [a,b] is:
    [tex]\frac{f(b)-f(a)}{b-a}[/tex]

    So in your case, the average rate of change is:
    [tex]\frac{f(2)-f(1)}{2-1}[/tex]
     
  6. Apr 8, 2006 #5
    Ok, I am not sure what to do with 2x^3 + x . So I subtracted it from the f(b) - f(a).
    If I had 2x^3 by it self, I can see just putting 2(2)^3 - 2(1)^3 / 2-1
    but the "+x" is confusing me
     
  7. Apr 8, 2006 #6
    I think I got it

    2(2)^3 + x - 2(1)^3 + x / 2-1

    =16-2+x+x / 1

    =14+2x

    =-2x + 14

    x = -7
     
  8. Apr 8, 2006 #7

    Galileo

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    So you can solve it if the function is 2x^3, but not if it's 2x^3+x? What's the difference, conceptually?

    f(x)=2x^3+x, so what is f(2)? And what is f(1)?
     
  9. Apr 8, 2006 #8

    BobG

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    Calculate f(2). Calculate f(1). Subtract the result of f(1) from f(2).

    The solution for f(2) is not 16+x. You have to substitute '2' for x everywhere it appears, so the solution for f(2) is 16+2.

    Also, your algebra is wrong (in addition to being not applicable in this case). If you have:

    [tex](3x^2 + 3x) - (2x^2 + 2x)[/tex]
    then the minus sign means both the 2x^2 and the 2x are negative:
    [tex]3x^2 + 3x - 2x^2 - 2x[/tex]
    [tex](3x^2 - 2x^2) + (3x - 2x)[/tex]
    etc.
     
  10. Apr 8, 2006 #9
    2(2)^3 + (2) -1 / 2-1

    16+2-1 / 2-1

    17/1

    17

    I'm sorry if I'm just not getting it
     
  11. Apr 8, 2006 #10

    Galileo

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    Alright, let's take some steps back.
    You are given a function f. It's a machine that eats a number and spits out a (usually different) number.
    f(x)=2x^3+x tells you the value of the function at each point, it's an equality that holds for each number x.
    For example:
    f(1)=2(1)^3+1=2+1=3
    f(5)=2(5)^3+5=2(125)+5=255

    So if you want to calculate [f(2)-f(1)]/(2-1) you have to calculate f(2) and f(1). I already did f(1) for you above. Now you do f(2) and calculate [f(2)-f(1)]/(2-1)
     
  12. Apr 8, 2006 #11
    2(2)^3 + (2) - 2(1)^3 +1 / 2-1

    =18-3 / 2-1

    =15/1

    =15
     
  13. Apr 8, 2006 #12

    Galileo

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    Right that's correct.

    BTW: Mind your brackets: -2(1)^3+1 is not the same as -(2(1)^3+1)
     
  14. Apr 8, 2006 #13
    Great! Thanks for your help!
    I have another one, maybe I should start a new post
     
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