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Math Help - Maxima and minima

  1. #1
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    Maxima and minima

    Hi All,
    Please help me to solve this:

    For the following function, find a point of maxima and a point of minima, if these exist:



    f(x) = 17x5 – 14x3 + 44.




    Thanks
    Arun
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  2. #2
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    Quote Originally Posted by arunkayal View Post
    Hi All,
    Please help me to solve this:

    For the following function, find a point of maxima and a point of minima, if these exist:



    f(x) = 17x5 14x3 + 44.

    Thanks
    Arun
    Well, for starters take the first derivative so you can see where the polynomial's critical points are.

    f'(x) = 85x^4 - 42x^2

    The roots of this function are the extrema of the original function. That is, set 0 = f'(x) and solve (hint recognize that 0 must be a root, so to find others, solve f'(x)=85x^2-42.)

    Take the next derivative and substitute in the critical points found above. If the result is negative then it's a max. If it's positive then it's a min. If it equals zero, then the point is neither max or min (throw it out), unless the whole original function is constant, which it is not in this case.
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  3. #3
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    Re:

    This problem can be summed up easily by following these four steps:

    1. Write the function
    2. Compute its derivative
    3. Set the derivative equal to zero and solve for x
    4. Take x coordinate(s) and insert back into the original function

    These steps are also known by Math Professors as finding the Critical Points.

    Best of Luck!
    Last edited by qbkr21; March 4th 2007 at 11:46 AM.
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