Derivation of the Most Probable Speed from

Maxwell's Velocity Distribution Equation

<= This is the distribution. Set the derivative equal to zero and solve for u to get the most probable speed.

I will begin by defining some numbers so that MathCad can make graphs.

Now let Mathcad take the derivative and set it equal to zero.

Now do a symbolic solve to get the three solutions to the cubic equation above.

Throw away the top and bottom answers as meaningless, and simplify the middle one.

<= Most probably speed.