Posted by **Jen** on Saturday, February 10, 2007 at 2:06pm.

P(x) = -(x-a)^4 (x-b)^3 (x-c)

where a>0, b<0, c>0, a<c

How do I sketch a graph of this?

Thanks

First you put the points a, b and c on the x-axis, doesn't matter precisely where, as long as it satisfies the conditions: a>0, b<0, c>0, a<c.

Then you use the fact that at a, b and c the function is zero. At b and c, the function changes sign, so it crosses the x-axis, but at x = a, there is no change of sign, there the function just touches the x-axis.

At x = c, the function crosses the x-axis at a nonzero angle. But at x = b, the fuction crosses the x-axis at zero angle. I.e. the function touches the x-axis there but unlike at point x = a, it does cross the x-axis.

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