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jennychan12

How can you tell just by looking at a graph whether a function is concave up or down?

  • one year ago
  • one year ago

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  1. Twis7ed
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    The concavity is basically where it "opens up" to. So, for example, f(x) = x^2 is concave up since it opens upwards while g(x) = -x^2 is concave down since it opens downwards.

    • one year ago
  2. wio
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    Draw/imagine the tangent line.

    • one year ago
  3. wio
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    If the tangent line is below it, then it is concave up.

    • one year ago
  4. wio
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    |dw:1363920994456:dw|

    • one year ago
  5. satellite73
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    imagine you are riding a bike along the curve from left to right if you are leaning left, it is concave up

    • one year ago
  6. jennychan12
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    ok, thanks. so if the tangent line is above the graph, it's concave down, right?

    • one year ago
  7. jennychan12
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    @satellite73 wow :) that actually made sense, and good analogy! :) so if ur leaning right, it's concave down?

    • one year ago
  8. satellite73
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    yes

    • one year ago
  9. satellite73
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    :"concave up" strikes me as devoid of meaning if it is "up" and "down" why bother with the "concave" part

    • one year ago
  10. johnweldon1993
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    yes..or imagine if you poured water into the line...would the water get collected...or just flow off?

    • one year ago
  11. satellite73
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    real definition is that any secant line lies entirely above the curve or anyway what you get when you write that in math

    • one year ago
  12. wio
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    |dw:1363921314201:dw|

    • one year ago
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