a farmer of a large farm of poultry announced that egg production per month follows the equation w=3m^1-m^3divided by m^2+10where w=total number of eggs produced per month and m=amount of kilograms of layers mash feed.

Question

a)find the rate of egg production for the farm

Answer 1

To find the rate of egg production for the farm, we need to take the derivative of the given equation with respect to m:

w = (3m - m^3) / (m^2 + 10)

dw/dm = (3(m^2 + 10) - (2m)(3m - m^3)) / (m^2 + 10)^2
dw/dm = (3m^2 + 30 - 6m^2 + 2m^4) / (m^2 + 10)^2
dw/dm = (2m^4 - 3m^2 + 30) / (m^2 + 10)^2

Therefore, the rate of egg production for the farm is dw/dm = (2m^4 - 3m^2 + 30) / (m^2 + 10)^2.