Derivative word problem

• Dec 5th 2009, 07:02 PM
s3a
Derivative word problem
Question:
"The velocity of a wave of length L in deep water is

v = K*sqrt(L/C + C/L)

where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?"

My work is attached (#43). (Page 10/14 of pdf file)

Any help would be greatly appreciated!
• Dec 5th 2009, 10:39 PM
[quote=s3a;418838]Question:
"The velocity of a wave of length L in deep water is

v = K*sqrt(L/C + C/L)

where K and C are known positive constants. What is the length of the wave that gives the minimum velocity?"

My work is attached (#43). (Page 10/14 of pdf file)

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hi, i havent looked at your work. but heres how i think it should go.

aim: find when dv/dl=0, this will give min/max for v with respect to l.

method:
so differentiate v with respect to l; $dv/dl = k^2(1/c -1/c^2)$ and now find l when dv/dl=0.

result:
you will get something along the lines of l^2=c^2.

conclusion:
idk.