4. The cost of producing x units of a product is C(x) = 0.004x2 – 9.6x + 7840. How many units should be produced to minimize the cost?

Answer 1

To find the minimum, take the derivative and set it equal to zero.

For C(x) = 0.004x² - 9.6x + 7840 you use the power rule to take the derivative. For the term "0.004x²", multiply the exponent "2" by the coefficient "0.004" and reduce the exponent by 1 to get "0.008x". For the term -9.6x, do the same except the exponent is "1" so the term becomes "-9.6". The derivative of the constant term "7840" is zero.

So C'(x) = 0.008x - 9.6

Setting it equal to zero:

0.008x - 9.6 = 0

0.008x = 9.6

x = 9.6/0.008 = 1200

Producing 1200 units will minimize the cost