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Math Help - critical points of maxima

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    critical points of maxima

    Critical points of maxima/ minima
    How can i determine the critical points of this function?
    f(x) = x^5 - 5x^3 - 20x - 2
    And thanks ahead
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Critical points of maxima/ minima
    How can i determine the critical points of this function?
    f(x) = x^5 - 5x^3 - 20x - 2
    And thanks ahead
    You will find critical points where f'(x) = 0. So:
    f'(x) = 5x^4 - 15x^2 - 20 = 0

    This is a "bi-quadratic" equation. To make things look simpler, let y = x^2. Then we need to solve:
    5y^2 - 15y - 20 = 0

    5(y^2 - 3y - 4) = 0
    5(y - 4)(y + 1) = 0

    So y = 4 and y = -1.

    Now, y = x^2 so we have x^2 = 4 and x^2 = -1.
    x^2 = 4
    x = -2 and x = 2.

    x^2 = -1
    has no real solutions.

    So the critical points are at x = -2, 2.

    -Dan
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