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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?"
Answer: L = C
My work is attached (#43). (Page 10/14 of pdf file)
Any help would be greatly appreciated!
Thanks in advance!

[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?"
Answer: L = C
My work is attached (#43). (Page 10/14 of pdf file)

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; $\displaystyle 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.