SOLUTION: Having trouble with the multiplicities concept: State the multiplicity of each of the zeros found in part (c). Describe how the multiplicity affects the behavior of the given fu

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Question 1058087: Having trouble with the multiplicities concept:
State the multiplicity of each of the zeros found in part (c). Describe how the multiplicity affects the behavior of the given function’s graph at each of these zeros.

What I have:
Original equation: f(x)=x^3-3x^2
I found the zeros after factoring the equation to: x^2(x-3)
Zeros of X are: (0,0) and (3,0)

I'm having a problem relating this to the multiplicities- any help would be greatly appreciated.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
You are pretty much on the right track.
+x%5E3+-+3x%5E2+=+%28x%5E2%29%28x-3%29+
So the zeros are:
0 (multiplicity 2)
3 (multiplicity 1)

The higher the multiplicity of a zero, the flatter the function is near that zero. This is easy to see using Calculus: for multiplicity of 2 or more, the derivative of f(x) (= rate of change of f(x)) will also have that zero.