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September 2nd, 2009, 02:28 AM   #1
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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 ... tled-5.jpg

thank you all so much in advance
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September 2nd, 2009, 07:31 AM   #2
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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.

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September 3rd, 2009, 02:16 AM   #3
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Re: Application of differentiation ! HELLP !!

thankk you !
i was so close xD
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September 3rd, 2009, 08:06 AM   #4
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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?
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March 3rd, 2017, 10:27 PM   #5
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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?

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March 3rd, 2017, 10:33 PM   #6
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Quote:
Originally Posted by KekkoMenny View Post
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?

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$T=\dfrac{\sqrt{4+x^2}}{3}+\dfrac{3-x}{5} = $

$\dfrac 5 5 \dfrac{\sqrt{4+x^2}}{3} + \dfrac 3 3 \dfrac{3-x}{5} = $

$\dfrac{5\sqrt{4+x^2}}{15} + \dfrac{3(3-x)}{15} = $

$\dfrac{5\sqrt{4+x^2} + 9-3x}{15}$
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March 4th, 2017, 08:34 PM   #7
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Maybe I didn't explain my self correctly, how did you get from to

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March 4th, 2017, 08:52 PM   #8
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Quote:
Originally Posted by KekkoMenny View Post
Maybe I didn't explain my self correctly, how did you get from to

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he took the derivative of this expression, set it equal to zero, and simplified it a bit so just this piece is set equal to zero.
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