# How do you graph #f(x)=x^4-3x^2+2x#?

I assume that you want to graph this without technology.

The graph is at the end of the solution. (I believe it's more instructive to not have it to start.)

If you prefer, use a factor table.

Whichever method you use, you'll find that:

Now sketch the graph (It may take a couple of rough sketches first:

graph{y=x^4-3x^2+2x [-10, 10, -5, 5]}

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To graph the function ( f(x) = x^4 - 3x^2 + 2x ), you can follow these steps:

- Find the critical points by setting the derivative of the function equal to zero and solving for ( x ).
- Determine the intervals where the function is increasing or decreasing by analyzing the sign of the derivative.
- Find the local maximum and minimum points, if they exist, by analyzing the sign changes in the derivative.
- Determine the intervals where the function is concave up or concave down by analyzing the sign of the second derivative.
- Find the inflection points, if they exist, by analyzing the sign changes in the second derivative.
- Use this information to sketch the graph of the function.

Would you like to see the detailed calculations for these steps?

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