As far as I'm aware, the explanation went like this;
Firstly, Plank established that the energy cost of making a specific frequency of light increased exponentially as frequency increased. This can be explined in two ways;
- Plank's equation, E = hf, could also be written E = hc/λ. (as f = c/λ) As 'c' is constant, when λ -> 0, (frequency increases), E -> ∞
- If one viewed the atom as an antennae, the frequency of the photon could be seen as an inverse function of the speed of the electron (as work function and mass are constant in this secnario, all excess energy imparted to the electron would be converted into kinetic energy). Therefore, for frequency to increase past a certain point, the electron has to approach relativistic speeds, where the energy cost for a speed increase rises exponentially.
As such, by establishing the exponential growth of energy cost, plank hypothesised that, when the predominant frequency of the black body shifted past a certain point, the energy cost to make that frequency outstripped the energy from the increase of heat of the black body. (Increasing the heat shifts the predominant freuqency). As such, the graph would peak and then decline, as the total intensity of the light decreased past that critical point.
Then again, I could be wrong. Consult a physics authority.