My Math Forum Finding Critical Numbers

 Calculus Calculus Math Forum

 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^9-7x^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 $f(x)= x^{10}e^{-7x}$, then $f'(x)= (10x^9- 7x^{10})e^{-7x}$. You should also know that $e^{-7x}$ can never be 0 so we must have $10x^9- 7x^{10}= 0$ Surely solving that is not so difficult! One method is, as jks said, is to factor out $x^9$: $x^9(10x- 7)= 0$. 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 $10x^9= 7x^{10}$. If $x\ne 0$, you can divide both sides by $x^9$.

 Tags critical, finding, numbers

« integral | find »

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post jkh1919 Calculus 10 July 24th, 2012 09:46 PM lovetolearn Calculus 1 April 5th, 2012 08:44 PM steelcurtain11 Calculus 2 November 1st, 2011 07:51 PM Calc12 Calculus 9 December 14th, 2010 09:18 PM lovetolearn Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top