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Math Help - how do i do this?

  1. #1
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    how do i do this?

    consider f(x) = e^-xsinx

    a)graph from -pi to 3pi/2.. DONE
    b)Use the graph of f to approxiamate a positive value of x past which the value of f is less than 0.10.. Don't get this??
    c)use calculus to find the POI on the interval[0, pi].. Do I jsut take the 2nd derivative and fidn the zeros??
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  2. #2
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    Quote Originally Posted by elpermic View Post
    consider f(x) = e^-xsinx

    a)graph from -pi to 3pi/2.. DONE
    b)Use the graph of f to approxiamate a positive value of x past which the value of f is less than 0.10.. Don't get this??
    c)use calculus to find the POI on the interval[0, pi].. Do I jsut take the 2nd derivative and fidn the zeros??
    b) There will be a value of on the x axis such that for values greater than x, the curve of the graph is always less than 0.1 on the y axis. You just have to name this point.

    c) No. When a 2nd derivative is equal to zero, you get no information about the graph. When f''(x) is less than 0, you have a local maximum at x. When f''(x) is greater than 0, you have a local minimum at x. However an inflection point is where the graph changes concavity. It increases, reaches a critical point, then increase further, or vice versa! Can you think of a way to find these?
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elpermic View Post
    consider f(x) = e^-xsinx

    a)graph from -pi to 3pi/2.. DONE
    b)Use the graph of f to approxiamate a positive value of x past which the value of f is less than 0.10.. Don't get this??
    c)use calculus to find the POI on the interval[0, pi].. Do I jsut take the 2nd derivative and fidn the zeros??
    Im not really sure what b) is asking either, maybe to use the graph of f(x) to "guess" what values of x make 0<f(x)<1/10?

    For c) what is POIs? Points of inflection would be the logical assumption.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Mush View Post
    c) No. When a 2nd derivative is equal to zero, you get no information about the graph. When f''(x) is less than 0, you have a local maximum at x. When f''(x) is greater than 0, you have a local minimum at x. However an inflection point is where the graph changes concavity. It increases, reaches a critical point, then increase further, or vice versa! Can you think of a way to find these?
    ...is this neccessarily true? Consider f(x)=x^2...by your assumption since f''(x)>0~~\forall x every value of x is a maximum? And the zeros do give us useful information, because supposing that f'' is continuous the change of signs you mentioned will only occur at points where the second derivative is zero.
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  5. #5
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    Quote Originally Posted by Mathstud28 View Post
    ...is this neccessarily true? Consider f(x)=x^2...by your assumption since f''(x)>0~~\forall x every value of x is a maximum? And the zeros do give us useful information, because supposing that f'' is continuous the change of signs you mentioned will only occur at points where the second derivative is zero.
    It is true if the first derivative is zero, which I assumed the OP was aware. Perhaps that was too big an assumption to make.

    Yes you're right, the 2nd derivative being equal to zero definitely rules out certain occurences, but it isn't useful in determining what HAS occured.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Mush View Post
    It is true if the first derivative is zero, which I assumed the OP was aware. Perhaps that was too big an assumption to make.

    Yes you're right, the 2nd derivative being equal to zero definitely rules out certain occurences, but it isn't useful in determining what HAS occured.
    Im sorry, I was under the impression that the OP was attempting to find points of inflection (POI).
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