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Math Help - x^3 + 2x^2

  1. #1
    s3a
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    x^3 + 2x^2

    I know how to graph x^3 and x^2 but this confuses me a little bit. I am guessing this is a cubic function but can someone please help me graph this function manually?

    Thanks in advance!
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  2. #2
    Member eXist's Avatar
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    Factor it:

    x^2(x + 2)

    Solve for the zeroes:

    x = 0
    x = -2

    Make a sign chart to see what the slopes are outside of those points. Graph to the best of your ability.

    That's what I would do, Chad
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by s3a View Post
    I know how to graph x^3 and x^2 but this confuses me a little bit. I am guessing this is a cubic function but can someone please help me graph this function manually?

    Thanks in advance!
    f(x)=x^3+2x^2=x^2(x+2)=0\Rightarrow\text{ zeros at }x=0,-2

    f'(x)=2x^2+4x=2x(x+2)=0\Rightarrow\text{ critical numbers at }x=0,-2

    Now, can u find the intervals when f is increasing and decreasing?
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  4. #4
    s3a
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    So I cannot tell how it will look like but only where it is positive or negative?
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by s3a View Post
    So I cannot tell how it will look like but only where it is positive or negative?
    Exactly! If the slope (the derivative) is negative, you know that the function is decreasing: meaning that it is falling as you move to the right.

    Similarily, the function is increasing if the value of the derivative is positive.

    So, with a couple of points, and this knowledge, you can sketch a pretty decent curve!
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