Question: Maximizing Planck's Intensity Function

I am attempting to maximize Planck's intesnity function for any given temperature T with respect to lambda. The function is as follows:

Iy = (2*h*c^2)/(lambda^5*(e^(hc/(lambda*k*T))-1))

 

My initial attempt was to simply take the derivative of this function with respect to labda, set it equal to zero, and then solve for lamda. Theoretically this should give me the value of lambda that maximizes the intesity with respect to the constants / values h, c, k, and T (where T is temperature).

 

However doing this in maple just leads to the result "warning, solutions may have been lost".

 

Does anyone know how I can go about maximizing this?

 

Thanks!

Please Wait...