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Math Help - Max or Min

  1. #1
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    Max or Min

    The height of an object, h(t), is determined by the formula
    h(t) = 16t2 + 256t, where t is time, in seconds. Will the object reach a maximum or a minimum? Explain or show your reasoning.


    I have trouble with questions like this when the value of the variable is not given.

    How can I find the answer without having to graph the given function?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    The height of an object, h(t), is determined by the formula
    h(t) = 16t2 + 256t, where t is time, in seconds. Will the object reach a maximum or a minimum? Explain or show your reasoning.

    I have trouble with questions like this when the value of the variable is not given.

    How can I find the answer without having to graph the given function?
    You should recognise the equation as a parabola. And you should know how to find the turning point of a parabola.
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  3. #3
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    Are you...

    Quote Originally Posted by mr fantastic View Post
    You should recognise the equation as a parabola. And you should know how to find the turning point of a parabola.
    Are you saying that I should graph the given function?
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  4. #4
    Super Member 11rdc11's Avatar
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    No just take the derivative and use the first derivative test to see when it is a max or min or you could complete the square too. Why the large red font?
    Last edited by 11rdc11; September 24th 2008 at 07:04 PM.
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  5. #5
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    Quote Originally Posted by magentarita View Post
    Are you saying that I should graph the given function?
    No. But obviously if you're going to draw a graph their are features you try to calculate, including coordinates of the turning point. You don't have to draw the graph to get the coordinates.

    Using symmetry, the t-coordinate of the turning point lies half-way between the t-intercepts. Do you know how to find it. Once you have the t-coordinate of the turnng point, how to get the h-coordinate shuld be clear. And it's a negative parabola (coefficient of squared term is negative). So the turning point is a maximum.
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  6. #6
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    Quote Originally Posted by magentarita View Post
    The height of an object, h(t), is determined by the formula
    h(t) = –16t2 + 256t, where t is time, in seconds. Will the object reach a maximum or a minimum? Explain or show your reasoning.

    I have trouble with questions like this when the value of the variable is not given.

    How can I find the answer without having to graph the given function?
    You are not asked to find the maximum or minimum, but just to identify if the given function has a max or min.

    You should recognise that h(t) is a parabola opening downwards, and hence this has a maximum. Also you should know that the maximum occurs midway between the roots, which in this case are obvious.

    RonL
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  7. #7
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    h(t) = 16t2 + 256t

    First derivative: -32t+256
    Second derivative: -32 <----this is negative, graph is a parabola, concave DOWN
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  8. #8
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    Quote Originally Posted by lewisb13 View Post
    h(t) = 16t2 + 256t

    First derivative: -32t+256
    Second derivative: -32 <----this is negative, graph is a parabola, concave DOWN
    This is a pre-calculus forum, so methods relying on diffrentiation are not helpfull or in this case needed.

    RonL
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  9. #9
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    derivatives...

    Quote Originally Posted by 11rdc11 View Post
    No just take the derivative and use the first derivative test to see when it is a max or min or you could complete the square too. Why the large red font?
    We are not doing derivatives in our precalculus class.

    I like to type using big words.
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  10. #10
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    How about....

    Quote Originally Posted by mr fantastic View Post
    No. But obviously if you're going to draw a graph their are features you try to calculate, including coordinates of the turning point. You don't have to draw the graph to get the coordinates.

    Using symmetry, the t-coordinate of the turning point lies half-way between the t-intercepts. Do you know how to find it. Once you have the t-coordinate of the turnng point, how to get the h-coordinate shuld be clear. And it's a negative parabola (coefficient of squared term is negative). So the turning point is a maximum.
    How about if I graph the function y = = 16t^2 + 256t?

    We are not doing derivatives in our precalculus class.





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  11. #11
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    But....

    Quote Originally Posted by CaptainBlack View Post
    You are not asked to find the maximum or minimum, but just to identify if the given function has a max or min.

    You should recognise that h(t) is a parabola opening downwards, and hence this has a maximum. Also you should know that the maximum occurs midway between the roots, which in this case are obvious.

    RonL

    How about if I graph the function y = = 16t^2 + 256t?

    We are not doing derivatives in our precalculus class.
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  12. #12
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    Look.....

    Quote Originally Posted by lewisb13 View Post
    h(t) = 16t2 + 256t

    First derivative: -32t+256
    Second derivative: -32 <----this is negative, graph is a parabola, concave DOWN
    How about if I graph the function y = = 16t^2 + 256t?

    We are not doing derivatives in our precalculus class.
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  13. #13
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    ok

    Quote Originally Posted by mr fantastic View Post
    No. But obviously if you're going to draw a graph their are features you try to calculate, including coordinates of the turning point. You don't have to draw the graph to get the coordinates.

    Using symmetry, the t-coordinate of the turning point lies half-way between the t-intercepts. Do you know how to find it. Once you have the t-coordinate of the turnng point, how to get the h-coordinate shuld be clear. And it's a negative parabola (coefficient of squared term is negative). So the turning point is a maximum.
    A negative parabola opens DOWNWARD.

    A positive parabola opens UPWARD.

    The downward parabola = minimum point...Is this true?

    The upward parabola = maximum point...Is this true?

    Thanks
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  14. #14
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    ok

    Quote Originally Posted by CaptainBlack View Post
    You are not asked to find the maximum or minimum, but just to identify if the given function has a max or min.

    You should recognise that h(t) is a parabola opening downwards, and hence this has a maximum. Also you should know that the maximum occurs midway between the roots, which in this case are obvious.

    RonL
    I fully understand.

    Thanks
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  15. #15
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by magentarita View Post
    We are not doing derivatives in our precalculus class.

    I like to type using big words.

    O ok well in that case you can find the vertex like I said earlier by completing the square. Also remember a negative parabola opens down.
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