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.