grade 12 AP calculus

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for f(x= -1/4x4-1/3x3+2x, use analytic method to find the exact intervals on which the function is a)increasing, b)decreasing, c)concave up, d)concave down, then find any e)local extreme values, f)inflection points

  • grade 12 AP calculus -

    y = -1/4 x^4 - 1/3 x^3 + 2x
    y' = -x^3 - x^2 + 2
    y'' = -3x^2 - 2x

    inflection where y''=0: x=0, -2/3
    local extrema where y'=0 and y''≠0: x=1
    increasing where y'>0: x<1
    decreasing where y'<0: x>1
    concave up where y''>0: -2/3 < x < 0
    concave down elsewhere

  • grade 12 AP calculus -

    how did you factor y' for this question?

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