solution:the total cost function of a firm is given by C=.04q^3-.9 q^2+10q+10.find slope of average cos?
On November 1, Able Corporation purchased a six-month insurance policy for the Baylor Agency for $3000.
To calculate the slope of the average cost, you first need to understand the relationship between the average cost and the total cost functions.
The average cost (AC) is given by the equation:
AC = C(q) / q,
where C(q) is the total cost function and q is the quantity produced.
In your case, the total cost function is given as C = 0.04q^3 - 0.9q^2 + 10q + 10.
To find the slope of the average cost, you need to differentiate the average cost function with respect to quantity (q). Let's calculate it step by step:
Step 1: Calculate the derivative of the total cost function, C(q), with respect to quantity (q).
dC(q)/dq = d(0.04q^3 - 0.9q^2 + 10q + 10)/dq,
Taking the derivative term by term, we get:
dC(q)/dq = 0.12q^2 - 1.8q + 10.
Step 2: Substitute the derivative of the total cost function into the formula for the slope of the average cost.
Slope of AC = (dC(q)/dq) / q.
Substituting the derivative obtained in step 1, we get:
Slope of AC = (0.12q^2 - 1.8q + 10) / q.
So, the slope of the average cost (AC) for the given total cost function is (0.12q^2 - 1.8q + 10) / q.