SOLUTION: Please show work Consider the function f(x)=x^5-x^3 Determine the behaviors as x→∞ and as x→-∞ Find all zeros. What is the multiplicity of roots (z

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Question 1020275: Please show work
Consider the function
f(x)=x^5-x^3
Determine the behaviors as x→∞ and as x→-∞
Find all zeros. What is the multiplicity of roots (zeros)?
When will the function cross the x-axis?
When will it cross the y-axis?

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Let's do some modification.


So as x get large in the positive direction, the right hand side is positive and the left hand term is positive so,

SImilarly, as x get large in the negative direction, the right hand side is still positive and the left hand term turns negative so,

.
.
.
Factor even more,


So there are zeros at ,,.
The root at has multiplicity of 3.
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.
.
Odd multiplicity on the zero root means it crosses three times.
.
.
.
When ,

(0,0)
.
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.
.

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