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swin2013

  • 2 years ago

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

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  1. swin2013
    • 2 years ago
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    |dw:1354148967410:dw| a) f(2) - positive b) f'(2) - ? c) f''(2) - ?

  2. swin2013
    • 2 years ago
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    @zepdrix

  3. zepdrix
    • 2 years ago
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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.

  4. zepdrix
    • 2 years ago
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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?

  5. swin2013
    • 2 years ago
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    |dw:1354149764955:dw|

  6. swin2013
    • 2 years ago
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    lol it's suppose to look like a the tip of a parabola

  7. zepdrix
    • 2 years ago
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    So a horizontal line represents what kind of slope? :D

  8. swin2013
    • 2 years ago
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    f'(2)

  9. zepdrix
    • 2 years ago
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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

  10. swin2013
    • 2 years ago
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    so neither are postive or negative?

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

  12. zepdrix
    • 2 years ago
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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. \[f''>0 \qquad \rightarrow \qquad \text{Concave Up}\]\[f''<0 \qquad \rightarrow \qquad \text{Concave Down}\]

  13. zepdrix
    • 2 years ago
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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''?

  14. swin2013
    • 2 years ago
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    it's increasing?

  15. zepdrix
    • 2 years ago
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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.

  16. swin2013
    • 2 years ago
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    so f(2) is negative, f'(2) is positive, therefore f''(2) is also positive :D

  17. zepdrix
    • 2 years ago
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    Why was f'(2) positive? :o

  18. zepdrix
    • 2 years ago
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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).

  19. zepdrix
    • 2 years ago
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    f(2) Negative f'(2) Zero f''(2) Positive

  20. swin2013
    • 2 years ago
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    ohhh... it's because they asked if they're positive or negative lolll

  21. zepdrix
    • 2 years ago
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    Yah, these kinds of uhhh graphs dealing with derivatives can be quite tricky c:

  22. swin2013
    • 2 years ago
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    Lolll ahhh well thank you again!! you're a life saverrrr!

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