Maximizing Absorption Coefficient: Optoelectronic Equation Homework

[leftovergold]

Homework Statement

Given the following equation for absorption coefficient in terms of frequency, find the wavelength that gives the maximum value of absorption coefficient.

The question: http://i.imgur.com/1jYg8.png

Homework Equations

Here is the equation: http://i.imgur.com/XUnHC.gif

The Attempt at a Solution

I am not sure how to begin this question. My initial guess is to use the "take the derivative and set equal to zero" method to find the maximum however this equation is out of my understanding for that method. I should note I understand the equation and all constants, just not what the question is asking for me to do.

Not looking for a solution here but just a suggestion on how to approach this question. Thank you.

 

[gneill]

You could use a programming method to find a maximum, or plot the function and find a maximum graphically. Otherwise, yes, the approach would be to differentiate and set equal to zero in the usual fashion.

Note that there are only two terms in the equation that appear to depend upon the frequency. So throw everything else away. That should make the derivative look a bit less daunting.