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September 2nd, 2009, 02:28 AM  #1 
Newbie Joined: Sep 2009 Posts: 3 Thanks: 0  Application of differentiation ! HELLP !!
A bush walker can walk at 5km/h through clear land and 3km/h through bushland. If she has to get from point A to point B following a route indicated at right, find the value of x so that the route is covered in a minimum time. (note: time=distance/speed) im sorry i didnt know how to upload a picture on to this post , so i have posted a link with my question ! http://i188.photobucket.com/albums/z106 ... tled5.jpg thank you all so much in advance 
September 2nd, 2009, 07:31 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond  Re: Application of differentiation ! HELLP !!
Time = distance/speed, let be time, so Derivative: To minimize time we set the numerator of the above equal to zero: , since distance is always positive we do not consider the negative root. 
September 3rd, 2009, 02:16 AM  #3 
Newbie Joined: Sep 2009 Posts: 3 Thanks: 0  Re: Application of differentiation ! HELLP !!
thankk you ! i was so close xD 
September 3rd, 2009, 08:06 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,809 Thanks: 2150 
Below the text box, there's an "Upload attachment" button! If you were so close, how come you didn't originally post the work you'd already done?

March 3rd, 2017, 10:27 PM  #5 
Newbie Joined: May 2015 From: Australia Posts: 10 Thanks: 0 
Sorry for posting on a 8 years old post, but I had the same question in my textbook, and I get how you find , but how did you derived? Thanks. 
March 3rd, 2017, 10:33 PM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 2,495 Thanks: 1370  Quote:
$\dfrac 5 5 \dfrac{\sqrt{4+x^2}}{3} + \dfrac 3 3 \dfrac{3x}{5} = $ $\dfrac{5\sqrt{4+x^2}}{15} + \dfrac{3(3x)}{15} = $ $\dfrac{5\sqrt{4+x^2} + 93x}{15}$  
March 4th, 2017, 08:34 PM  #7 
Newbie Joined: May 2015 From: Australia Posts: 10 Thanks: 0 
Maybe I didn't explain my self correctly, how did you get from to Thanks. 
March 4th, 2017, 08:52 PM  #8 
Senior Member Joined: Sep 2015 From: USA Posts: 2,495 Thanks: 1370  

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