Finding the Most Probable Frequency/Wavelength of Planck Functions

[sweetdreams12]

I came across this question and though I've looked it up but I haven't found anything concrete and in truth confuses me more. It was posed by my lecturer and it is:

For the Planck function Bv(t), what is the most probable frequency vp at a given temperature? Similarly for the Planck function Bλ(t), what is the most probable wavelength λp at a given temperature and are the two results consistent with each other?

I know for the second one that I need dB/dλ = 0 but then what do I do? Detailed help would be most appreciated :)

 

[Adrmay]

For the first question, the most probable frequency vp at a given temperature is given by the peak of the Planck function Bv(t). The peak occurs when the derivative of the Planck function is equal to zero. For the second question, the most probable wavelength λp at a given temperature can be found by setting the derivative of the Planck function Bλ(t) to zero. The two results should be consistent with one another since they are both derived from the same Planck function.