The general relationships f’(alpha(max)) x F(alpha(max)) = -Q(x(max)) and (d alpha/dx(max)) = f(alpha(max))/f’(alpha(max)) have been established, for a non-iosthermal thermogravimetric rate equation, where f(alpha) is the conversion function, F(cr) is the conversion integral and Q(x)= x(2)e(x)p(x). For an nth order reaction, the dependence x(max) = x(max) (n, AE/beta R) is analysed by solving of a transcendental equation, using an iterative method. The temperature integral, p(x), was inverted using a minimax approximation, with a relative percentage error of 2.13 x 10(-4) in the interval x is an element of [5,92].