Question

find the minimum velocity of the following?

Answer 1

\[v = k \sqrt{(\lambda/c) + (c/\lambda)} \], where c and k are positive constants and v is speed and \[\lambda\] is the wave of wavelength travelling in deep watere

Answer 2

Writing L for lambda, if we differentiate we have

dv/dL = k ( 1/c - c/L^2 ) / 2.sqrt( ... )

and hence this is zero if and only if
\[ \lambda = \pm c \]

Now evaluate the nature of those two points (local max? min? ... )