Question

To produce a soft drink, the following production cost per day is given: C = 100 + 9q - 0.01q^2. Calculate dC/dq.

Answer 1

To calculate the derivative dC/dq of the production cost function C = 100 + 9q - 0.01q^2, apply the rules of differentiation to obtain dC/dq = 9 - 0.02q.

Step-by-step explanation:

The student is asked to calculate the derivative of the production cost function C = 100 + 9q - 0.01q^2 with respect to the quantity q. The derivative, dC/dq, represents the rate of change of the production cost with respect to the quantity of the soft drink produced. To find this, we apply the rules of differentiation to each term of the function:

• The derivative of a constant like 100 is 0.
• The derivative of 9q with respect to q is 9.
• The derivative of -0.01q^2 with respect to q is -0.02q.

Therefore, combining all these results, the derivative dC/dq is:

dC/dq = 9 - 0.02q