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Math Help - Finding point of max. and min.

  1. #1
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    Question Finding point of max. and min.

    hello Friends,
    I cant solve out this problem.
    For the following function, find a point of maxima and point of minima,if these exist:
    f(x)=17x^5-14x^3+44

    Thanks
    Harshal.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by harshal54321 View Post
    hello Friends,
    I cant solve out this problem.
    For the following function, find a point of maxima and point of minima,if these exist:
    f(x)=17x^5-14x^3+44

    Thanks
    Harshal.
    Differentiate and classify the zeros of f'(x)=0.

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

    so the solutions of f'(x)=0 are x=0, and +/- sqrt(42/85).

    Now the second derivative f''(x) = 340 x^3 - 84 x, so the second derivative
    test tells us that x=+sqrt(42/85) is a local minimum, and x=-sqrt(42/85) is a
    local maximum.

    f''(0)=0, so we need to classify x=0 by other means: As f(x) is an odd order
    polynomial it has an equal number of maxima and minima, but here we have
    three roots for f(x)=0, so f(0) must be a point of inflection.

    RonL
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