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.
a)find the rate of egg production for the farm
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.