calculus I

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hi! can someone please help me ... question: a)find the intervals on which f is increasing or decreasing b)find the local max and min values of f c)find the intervals of concavity and the inflection points f(x)=2x^3+3x^2-6x+1 i know its a long problem but i really need help

  • calculus I -

    So first of all
    y' = 6x^2 + 6x - 6
    y'' = 12x + 6

    for local max/min y'=0
    6x^2 + 6x - 6 = 0
    x^2 + x - 1 = 0
    x = (-1 ± √5)/2

    sub that into the function to get the max/min, you do the arithmetic.

    for pts of inflection, 12x+6=0
    x=-1/2
    sub that back into the function to get the point of inflection. You do the arithm.

    for concave up y'' > 0, for down y'' < 0

    for 12x+6 > 0 concave up, or x > -1/2 concave up
    for 12x+6< 0 concave down, or x < -1/2 concave down.

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