Question

a model used for the yield y of an agricultural crop as a function of the nitrogen level n in the soil is given by where k is a positive constant. what nitrogen level give the best yield?

Answer 1

The nitrogen level that gives the best yield in the given model is any nitrogen level, as there is no maximum or minimum point.

Step-by-step explanation:

The model used to represent the yield of an agricultural crop as a function of the nitrogen level in the soil is given by the equation y = kn, where k is a positive constant. To find the nitrogen level that gives the best yield, we need to maximize the yield function y.

To maximize the yield function, we can take the derivative of y with respect to n and set it equal to zero. This will give us the critical points, which are the potential maximum or minimum points of the function. In this case, we only need to consider the maximum point. So, let's find the derivative of y.

dy/dn = k

Setting this equal to zero, we get k = 0. Since k is a positive constant, there is no critical point. This means that the yield function does not have a maximum or minimum point. Therefore, any nitrogen level will give the same yield.