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.
.
.
.
Odd multiplicity on the zero root means it crosses three times.
.
.
.
When ,
(0,0)
.
.
.
.
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