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swin2013 Group Title

For the function graphed, are the following nonzero quantities positive or negative?

  • one year ago
  • one year ago

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  1. swin2013 Group Title
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    |dw:1354148967410:dw| a) f(2) - positive b) f'(2) - ? c) f''(2) - ?

    • one year ago
  2. swin2013 Group Title
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    @zepdrix

    • one year ago
  3. zepdrix Group Title
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    f'(2) represents the SLOPE of the function at that point. So let's draw the line tangent to the curve at f(2) to see what it looks like.

    • one year ago
  4. zepdrix Group Title
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    |dw:1354149736096:dw| It's kind of hard to tell, based on the sloppy drawing lolol. Was it supppose to be slanted down like that? Or is it suppose to be flat on the bottom at 2?

    • one year ago
  5. swin2013 Group Title
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    |dw:1354149764955:dw|

    • one year ago
  6. swin2013 Group Title
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    lol it's suppose to look like a the tip of a parabola

    • one year ago
  7. zepdrix Group Title
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    So a horizontal line represents what kind of slope? :D

    • one year ago
  8. swin2013 Group Title
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    f'(2)

    • one year ago
  9. zepdrix Group Title
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    f'(2) is zero :) we can tell that since we drew a tangent line. It is neither positive nor negative, right? :D

    • one year ago
  10. swin2013 Group Title
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    so neither are postive or negative?

    • one year ago
  11. swin2013 Group Title
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    except for f(2)? Which is negative.. lol i never meant to put postive

    • one year ago
  12. zepdrix Group Title
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    f'' is a little trickier. There are a couple ways we can determine if it's positive or negative. f'' tells us if the SLOPE is increasing or decreasing. But an easier way to maybe think about it is by referring back to the second derivative test. \[f''>0 \qquad \rightarrow \qquad \text{Concave Up}\]\[f''<0 \qquad \rightarrow \qquad \text{Concave Down}\]

    • one year ago
  13. zepdrix Group Title
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    We can use this information in reverse. In the given problem we KNOW that f(2) lies in an area that is CONCAVE UP. See how it's inside of a bowl shape? So what does that tell us about f''?

    • one year ago
  14. swin2013 Group Title
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    it's increasing?

    • one year ago
  15. zepdrix Group Title
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    Well... it tells us that f' is increasing c: But based on the little facts I printed a sec ago, it tells us that f'' is GREATER THAN ZERO right? :D or in other words, Positive.

    • one year ago
  16. swin2013 Group Title
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    so f(2) is negative, f'(2) is positive, therefore f''(2) is also positive :D

    • one year ago
  17. zepdrix Group Title
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    Why was f'(2) positive? :o

    • one year ago
  18. zepdrix Group Title
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    We determined that the slope is zero. It will increase towards the positive as we move to the right, but it is zero at the point f(2).

    • one year ago
  19. zepdrix Group Title
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    f(2) Negative f'(2) Zero f''(2) Positive

    • one year ago
  20. swin2013 Group Title
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    ohhh... it's because they asked if they're positive or negative lolll

    • one year ago
  21. zepdrix Group Title
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    Yah, these kinds of uhhh graphs dealing with derivatives can be quite tricky c:

    • one year ago
  22. swin2013 Group Title
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    Lolll ahhh well thank you again!! you're a life saverrrr!

    • one year ago
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