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Calc 1, f'(x) > 0 if x < 0 ? What does this mean?

  1. Feb 14, 2012 #1
    My math calc 1 class starts just 10 minutes after my physics class ends and it's on the opposite side of campus and yesterday I had my first exam in physics and ended up missing the first 3 minutes of my math class lecture. I copied the notes from the board, but didn't hear what he was saying about the graph. He's an excellent professor, but without hearing what he was saying, I can't figure out what the notes are talking about.

    Can anyone look at this graph and the formula and decipher what concept/lesson the professor was describing?


    calc.jpg


    perhaps f(0) = -2 doesn't correspond to anything on this graph..it could be from somthing else he had already erased before I got to class, i just don't know.

    So i'm trying to figure out what it all means.
     
  2. jcsd
  3. Feb 14, 2012 #2

    SammyS

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    The title of this thread, f'(x) > 0 if x < 0 ? What does this mean? means that when x is negative, the slope f(x) (well, actually the slope of the line tangent to f(x)) is positive, as in the lower of the two graphs.
     
  4. Feb 14, 2012 #3

    HallsofIvy, thanks

    I quoted you to this thread because I asked for deletion of the other thread since I accidently posted it in the wrong forum section and didn't want to lose your response upon deletion. I'm reading your response now.
     
  5. Feb 14, 2012 #4

    tiny-tim

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    Hi LearninDaMath! :smile:

    (I assume you're ok with the main part …

    demonstrating how the sign of f' works, with two examples, one with f'' > 0 and one with f'' < 0 ?)


    I'll guess that that should read f''(0) = -2 :wink:
     
  6. Feb 14, 2012 #5
    I think I understand.

    So if I have any function, say, f(x) = 2x^2 + 5x

    and I take the derivative: f'(x) = 4x + 5

    then for any value of x I choose for the independent variable: say, x = -7,

    then f'(x) = 4(-7) + 5 = -23

    and so f'(x) < 0 so the slope of the tangent is negative at x = -7

    Is this a correct description of the concept here?

    Hi Tiny-Tim,

    So the first three functions at the top of the notes should be double primes instead of regular functions?
     
    Last edited: Feb 14, 2012
  7. Feb 14, 2012 #6

    tiny-tim

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    Hi LearninDaMath! :smile:
    Yes, wherever f'(x) < 0, the slope is negative
    No, only the first one.

    The other two say that, on that particular graph (the top one), f'(x) is negative on the left, and positive on the right (as you can see from the graph).
     
  8. Feb 14, 2012 #7
    ah, moment of clarity, the notes make sense now :) thanks
     
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