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 Calculus Calculus Math Forum

 April 21st, 2016, 02:27 AM #1 Newbie   Joined: Apr 2015 From: Slovakia Posts: 5 Thanks: 0 Local extrema Hi, I have to find the local extrema of the function 2016-04-21 12_11_32-IMA2_9.png . But the problem is that as far as I know I have to find critical numbers first, but after I find first derivative. I get f'(x) = e^(3x+2y) *(6x-6y+8y^2); what should I do now? If I set it equal to 0, I am kind of lost. Last edited by Mrto; April 21st, 2016 at 02:55 AM. April 21st, 2016, 03:36 PM #2 Global Moderator   Joined: May 2007 Posts: 6,762 Thanks: 697 Your description is confusing. are x and y separate variables? In that case you have a surface, so it is not clear what you are looking for. April 23rd, 2016, 10:08 AM #3 Newbie   Joined: Apr 2015 From: Slovakia Posts: 5 Thanks: 0 Idk, its homework and the assignment only says "Find local extrems of function (function in op)" . We did simillar problem to this, we first derivated with respect to x, then with respect to y, then set both equal to 0 and found critial numbers. And then I dont remember and i dont have my book near me right now . April 23rd, 2016, 03:26 PM #4 Global Moderator   Joined: May 2007 Posts: 6,762 Thanks: 697 You want $\displaystyle \frac{\partial f(x,y)}{\partial x}\ and\ \frac{\partial f(x,y)}{\partial y}$ To save writing let $\displaystyle g(x,y)=e^{3x+2y}\ and\ p(x,y)=3x^2-6xy+6y^2$ You need to compute $\displaystyle \frac{\partial f(x,y)}{\partial x}=p(x,y)\frac{\partial g(x,y)}{\partial x}+g(x,y)\frac{\partial p(x,y)}{\partial x}\ and\ \frac{\partial f(x,y)}{\partial y}=p(x,y)\frac{\partial g(x,y)}{\partial y}+g(x,y)\frac{\partial p(x,y)}{\partial y}$. Since $\displaystyle \frac{\partial g(x,y)}{\partial x}=3g(x,y)\ and\ \frac{\partial g(x,y)}{\partial y}=2g(x,y)$, when you set things = 0, g(x,y) is a common factor and can be dropped. You should be able to do this. Thanks from Mrto Tags extrema, local Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mike1127 Calculus 2 March 22nd, 2016 12:17 AM CPAspire Pre-Calculus 2 March 27th, 2015 07:52 AM mastermind Calculus 1 February 27th, 2015 03:14 PM maluita659 Calculus 1 February 21st, 2014 12:02 PM crnogorac Calculus 1 December 24th, 2013 04:03 AM

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