7) A total-cost function is given by C(x)=2000(x2+2)1/3+700, where C(x) is the total cost, in thousands of dollars, of producing x items. Find the rate at which total cost is changing when 20 items have been produced.

8) The dosage for Carboplatin chemotherapy drugs depends on several parameters of the particular drug as well as the age, weight, and sex of the patient. For female patients, the formulas giving the dosage for such drugs are

D=0.85A(c+25)and c=(140y)72xw

where A and x depend on which drug is used, D is the dosage in milligrams (mg), c is called the creatine clearance, y is the patient's age in years, and w is the patient's weight in kilograms (kg).

8a) Suppose that a patient is a 45-year-old woman and the drug has parameters A= 5 and x= 0.6. Use this information to write formulas for D and c that give D as a function of c and c as a function of w

8b) Use your formulas from part (a) to compute dD/dc

8c) Use your formulas from part (a) to compute dc/dw

8d) Compute dD/dw

8e) Interpret the meaning of the derivative dD/dw in a few sentences.