Suppose the cost C(q) (in dollars) of producing a quantity q of a product
equals
C(q) = 500 + 2q +1/5q^2
The marginal cost M(q) equals the instantaneous rate of change of the
total cost. Find the marginal cost when a quantity of 10 items are being
produced.
To find the marginal cost when a quantity of 10 items are being produced, we need to find the derivative of the cost function C(q) with respect to q and evaluate it at q = 10.
Let's start by finding the derivative of C(q) with respect to q:
C'(q) = dC(q)/dq = 0 + 2 + (2/5)q
Now we can evaluate C'(10) by substituting q = 10 into the derivative:
C'(10) = 2 + (2/5)(10) = 2 + 4 = 6
So the marginal cost when a quantity of 10 items are being produced is $6.