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To prove this equation can exist or not hmm

  1. Nov 2, 2004 #1
    The question is : Find an F(x) where fprime(-1) = 1/2 , fprime(0) = 0 and fdoubleprime>0 if it doesnt exist prove why.

    I cannnot explain it that well but here i go, i feel there is no equation that can be made for this. For an equation for be concave up on all intervals it must be in the form Ax^multipleof2 + B^multipleof2 + C^multipleof2 + etc etc etc..... + Dx + E, where A and B and C... are positive constants I say this because f double prime will onyl be positive for all x if the second dirivitive has only positive constants or terms of x^multipleof2. Then the first dirivitive will leave you with x^odd number + a constant, f(-1) must be equal to 1/2, so it must be positive since x^oddnumber will be negative. but then when it says fprime(0) = 0 this cannot be because you will have 0^oddnubmer + constant.

    blah thats as far as i could take it im not sure if it makes sense.. but can someone help me on the correct path.
     
    Last edited: Nov 2, 2004
  2. jcsd
  3. Nov 2, 2004 #2

    shmoe

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    -not all functions are polynomials
    -a polynomial can be concave up everywhere and still have negative coefficients or odd powers, [itex]x^{2}-x-1[/itex] does all this
    -latex is a beautiful thing and will make your posts legible with little effort, see https://www.physicsforums.com/misc/howtolatex.pdf

    For your question, if [itex]f''(x)>0[/itex] for all [itex]x[/itex] what can you say about [itex]f'(x)[/itex]? Is it increasing? Decreasing? Neither?
     
  4. Nov 3, 2004 #3

    HallsofIvy

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    Since f'' is just the derivative of f', this exactly the same as:

    "Does there exist a function f, whose derivative is always positive, such that f(-1)= 1/2 and f(0)= 0". Since f ' is always positive, what does that tell you about f?
     
  5. Nov 3, 2004 #4
    I think HallsofIvy meant to put primes in front of those f's, but anyway... :)

    Think of it like this: The slope of a function is positive at -1, then it turns to zero at 0. Draw that out. What would a function like that look like? Increasing then not. So does this mean f can be concave up for all x?
     
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