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Math Help - Concave/inflection Points

  1. #1
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    Talking Concave/inflection Points

    Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.

    f(x)=x^3+3x^2+x+1

    My book has the answer:

    up is [-1, infinity)
    down is (- infinity, 2]
    inflection points (-1,2)

    I know you have to find the first and second derivative which is

    f'(x)=3x^2+6x+1
    f''(x)=6(x+1)

    I just don't know where to go from there..Thanks!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.

    f(x)=x^3+3x^2+x+1

    My book has the answer:

    up is [-1, infinity)
    down is (- infinity, 2]
    inflection points (-1,2)

    I know you have to find the first and second derivative which is

    f'(x)=3x^2+6x+1
    f''(x)=6(x+1)

    I just don't know where to go from there..Thanks!

    well youre right! Weve gotta find the second derivative. Lettss do it>



    [tex]f'(x)=3x^2+6x+1[tex], and f''(x)=6(x+1)

    good good good. so then the inflection point

    f''(x)=6(x+1)=0\Longleftrightarrow{x=-1}

    good good Now plugging back in the original formula gives us (-1,2).

    good good Concavity

    • x = a is a locally a minimum if f"(a) > 0,
    • x = a is a locally a maximum if f"(a) < 0; and
    Using a little noodle power, you can do the rest..........

    You can DO IT!!!!!!!!
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