contestada

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 =?

Respuesta :

The nitrogen level would give the best yield at N = 1

Given y =  (kN)/(1+N^2)

first step is to take the derivative

the derivative is [tex]y' = \frac{k - kN^2}{( 1 + N^2)^2}[/tex]

ON equating this value of y' to 0

we get

y' = k - k[tex]N^2[/tex] = 0

k ( 1 - N^2) = 0

After dividing the above equation with k

and then subtracting we get ;

N = ± 1

However N = 1 is the only possible answer since the nitrogen level can't be negative

thus the nitrogen level gives the best yield at N = 1

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