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im having so much trouble figuring out how to get these answers. i already know the answers i just need to figure out how to get them...

directions: find the points of inflection and discuss the concavity of the graph of the function...

1. f(x)=(1/2)x^4+2x^3
2. f(x)=x^3-6x^2+12x
3. f(x)=(1/4)x^4-2x^2
4. f(x)=2sinx+sin2x, [0,2ð)

  • calculus -

    f = 1/2 x^4 + 2x^3
    f' = 2x^3 + 6x^2
    f'' = 6x^2 + 12x

    f' = 0 at x=0,0,-3 so the possible mins/maxes are there
    f'' = 0 at 0,-2 so the inflection is there.

    At x=0, f'=0 and f''=0, so not a min/max -- inflection
    At x=-3, y'' > 0, so concave up (min)

    Proceed similarly with the others.

    rechneronline . de is a good grapher

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