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suneja Group Title

function f & g are both concave fns of a single variable. Neither fn is necessarily differentiable. is the fn defined by h(x)=f(x)+g(x) necessarily concave, necessarily convex or not necessarily either.

  • one year ago
  • one year ago

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  1. JakeV8 Group Title
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    I am thinking it would be "necessarily concave"... what do you think? I am still considering what impact comes from the fact that it says the functions f and g are not necessarily differentiable.

    • one year ago
  2. suneja Group Title
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    that wer my doubt area is.. cz wen u jst use the fact that f n g are concave u can show h is concave but wat difference does differentiability makes here

    • one year ago
  3. JakeV8 Group Title
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    yes... interesting. What would make f not differentiable but still allow it to be considered concave? There is the "easy" definition of concave as U shaped (bowl, open side up). But the definition based on derivatives depends, I would have thought, on the function being differentiable. Maybe you can imagine a non-differentiable function that still faces upward.... if you can imagine one, then a second similar upward facing function probably (but I hate guessing!!) can just be added to the first one without affecting concavity.

    • one year ago
  4. JakeV8 Group Title
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    certainly if you had f(x) = x^2 and g(x) = 2x^2, adding them to get h(x) = 3x^2 is still concave. (wait, am I totally backwards on concave? an upward parabola is concave up, right? Not convex? It's been awhile since I've done this sort of problem).

    • one year ago
  5. suneja Group Title
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    ya upward parabola is concave up

    • one year ago
  6. suneja Group Title
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    concave fns hav minima ie second differenciation is >0

    • one year ago
  7. JakeV8 Group Title
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    so, f(x) = x^2 is concave up, but it doesn't demonstrate non-differentiability. But I brought it up as a simpler example... adding 2 concave-up parabolas results in a 3rd up-facing parabola

    • one year ago
  8. suneja Group Title
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    v need to prove tis ... how shud i go abt it

    • one year ago
  9. JakeV8 Group Title
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    so, leaving aside the non-differentiable part for a sec, I'm pretty certain you could prove analytically that for any f(x) and g(x) that are concave up, h(x) is also concave up.

    • one year ago
  10. suneja Group Title
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    ya.

    • one year ago
  11. JakeV8 Group Title
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    do you actually have to prove this? Or just answer? Also, help me on this non-differentiable idea... what makes something non-differentiable? Is it that a derivative is undefined, like a section of vertical slope?

    • one year ago
  12. JakeV8 Group Title
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    |dw:1348929716882:dw|

    • one year ago
  13. JakeV8 Group Title
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    Do you think the made-up function in that diagram is considered concave but not differentiable because of the vertical slope piece in the middle? I don't really know...

    • one year ago
  14. JakeV8 Group Title
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    I just looked it up... it doesn't have to be this hard :)

    • one year ago
  15. suneja Group Title
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    a fn is not differential at "kink" ie corners so it shudnt be diff

    • one year ago
  16. suneja Group Title
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    |dw:1348930186324:dw| it wont be diff der

    • one year ago
  17. JakeV8 Group Title
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    an absolute value function is non-differentiable... f(x) = |x| is concave up... g(x) = |x + 2| is also... is f(x) + g(x) is concave?

    • one year ago
  18. JakeV8 Group Title
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    |dw:1348930353864:dw|

    • one year ago
  19. suneja Group Title
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    k tis makes sense:)

    • one year ago
  20. JakeV8 Group Title
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    Maybe... it's making my head hurt! with that absolute value example, does that h(x) qualify as concave up? It doesn't have a single minimum point, but the line across the bottom is a minimum area over that range, and the whole function does face up... just not sure about the definition of concave in a situation like this.

    • one year ago
  21. suneja Group Title
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    see a/c to the dat i hav they hav jst used tha fact dat f n g r concave all i want to knw is wat does tis phrase means " Neither fn is necessarily differentiable

    • one year ago
  22. JakeV8 Group Title
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    I think it just means that you cannot rely on differentiating the functions as a way of showing that h(x) is concave. You have to be able to realize what adding concave functions does WITHOUT trying to find the derivative of h(x) to answer about its concavity.

    • one year ago
  23. suneja Group Title
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    maybe

    • one year ago
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