1. ## 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?

2. Factor it:

$\displaystyle x^2(x + 2)$

Solve for the zeroes:

$\displaystyle x = 0$
$\displaystyle x = -2$

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

3. 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?

$\displaystyle f(x)=x^3+2x^2=x^2(x+2)=0\Rightarrow\text{ zeros at }x=0,-2$

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

Now, can u find the intervals when f is increasing and decreasing?

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

5. 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!