x^3 + 2x^2

**s3a** · September 1st 2009, 04:35 PM

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!

**eXist** · September 1st 2009, 04:46 PM

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

**VonNemo19** · September 1st 2009, 04:47 PM

Originally Posted by s3a

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?

**s3a** · September 4th 2009, 06:38 AM

So I cannot tell how it will look like but only where it is positive or negative?

**VonNemo19** · September 4th 2009, 07:06 AM

Originally Posted by s3a

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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