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Question 1020077: Please show all work.
Consider the function
f(x)=x^5-x^3
a Determine the behaviors as x→∞ and as x→-∞
b Find all zeros. What is the multiplicity of roots (zeros)?
c When will the function cross the x-axis? When will it cross the y-axis?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please show all work.
Consider the function
f(x)=x^5-x^3
a Determine the behaviors as x→∞ and as x→-∞
The highest power term determins the answer::
Since x^5 goes to +oo as x goes to +oo, f(x) goes to +oo
Since x^6 goes to -oo as x goes to -oo, f(x) goes to -oo
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b Find all zeros. What is the multiplicity of roots (zeros)?
Solve x^5-x^3 = 0
x^3(x^2-1) = 0
x = 0 with multiplicity 3
x = 1 with multiplicity 1
x = -1 with multtiplicity 1
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c When will the function cross the x-axis?
Solve x^5 - x^3 = 0 to answer that question.
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When will it cross the y-axis?
Let x = 0, then f(0) = 0
Ans (0,0)
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Cheers,
Stan H.
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