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November 6th, 2013, 09:14 AM   #1
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Finding Critical Numbers

Hello I got a question for finding critical numbers in a curve sketch.

Find all critical numbers:

f(x)=(x^10)e^-7x


I know that f'(x)(10x^9-7x^10)e^-7x

But im not sure what to do next..

Thanks in advance!
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November 6th, 2013, 10:14 AM   #2
jks
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Re: Finding Critical Numbers

Hi SamFe,

Factor out x^9.
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November 6th, 2013, 12:11 PM   #3
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Re: Finding Critical Numbers

I presume you know, although you did not say it, that "critical numbers" for a function are values of x at which f'(x)= 0 or the derivative does not exist.

Yes, if , then .

You should also know that can never be 0 so we must have

Surely solving that is not so difficult! One method is, as jks said, is to factor out : .
Of course, if the product of two numbers is 0, one or the other must be 0.

Another way to do it is to write it as . If , you can divide both sides by .
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