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reactor

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I have problem with determine the minimum speed in this problem , I think the the maximum speed equal to the average speed and the most probable speed can be obtain by derive equation and equally to zero .Is my solution correct?

The speed distribution function for N particles in a fixed volume is given by f (V) = AV(B - V)/B^3,

where V (>0) is the particle speed, and A and B are positive constants. Determine:

(a) The minimum speed Vmin and maximum speed Vmax.

b) The most probable speed where the probability density function is the largest.