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Calculus

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Consider f(x)=200+8x^3+x^4. find the intervals on which function is increasing or decreasing, the local max and minimu values, the intervals of concavity and the inflection points

  • Calculus -

    Increasing where f' > 0
    Decreasing where f' < 0

    f'(x) = 24x^2 + 4x^3 = 4x^2(6+x)

    Concave up where f'' > 0
    Concave down where f'' < 0

    f'' = 48x - 12x^2 = 12x(4-x)

    Max where f' = 0 and f'' < 0
    Min where f' = 0 and f'' > 0

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