Another use of distribution functions is determining the most-probable value, which is done by realizing that at the distribution maximum the derivative of the distribution function with respect to the variable of interest will be zero. Using this concept, determine the most probable value of x (0 ≤ x ≤ ∞) for the following function: 

P (x) = Cx² e^-ax2

Compare your result to x and x_rms when a = 0.3 (see example problem 29.13).