November 6th, 2013, 09:14 AM  #1 
Newbie Joined: Oct 2013 Posts: 17 Thanks: 0  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^97x^10)e^7x But im not sure what to do next.. Thanks in advance! 
November 6th, 2013, 10:14 AM  #2 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 Math Focus: Electrical Engineering Applications  Re: Finding Critical Numbers
Hi SamFe, Factor out x^9. 
November 6th, 2013, 12:11 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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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