# How do you solve this optimization question?

##
A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is

#y=(kN)/(1+N^2)#

where k is a positive constant. What nitrogen level gives the best yield?

#N=?#

A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is

where k is a positive constant. What nitrogen level gives the best yield?

##### 1 Answer

#### Explanation:

Take the first derivative with respect to

Equate to

The "best yield" would entail

If