A company knows that unit cost C and unit revenue R from the production and sale of x units are related by R^2/236000+5507 . Find the rate of change of revenue per unit when the cost per unit is changing by and the revenue is
To find the rate of change of revenue per unit when the cost per unit is changing, we need to find the derivative of the revenue function with respect to the cost per unit.
Given the revenue and cost relationship as R^2/236000+5507, we can rewrite it as R = √(236000C + 5507).
Now, let's differentiate the revenue function R with respect to the cost C using the chain rule of differentiation.
dR/dC = (1/2√(236000C + 5507)) * (236000)
Simplifying this derivative, we get:
dR/dC = 118000/√(236000C + 5507)
This gives us the rate of change of revenue per unit with respect to the cost per unit.