optimization circuit

Question

The average cost function, denoted as a(x), is defined as a(x) = c(x) / x, where c(x) represents the cost function, and x represents the number of units produced. The cost function is given as c(x) = 25000 + 100x + 4x^(3/2). What is the production level at which the average cost is minimized for the given cost function c(x) = 25000 + 100x + 4x^(3/2)?

Answer 1

Try taking the derivative of a(x) = c(x)/x = 25000/x+100+4x^(1/2)

a maximum or minimum will usually occur at a critical point (that is, when a'(x) = 0),

so you should solve a'(x) = 0 for x, then determine whether a(x) achieves a minimum or maximum at that x value. To do this, you could use the first derivative or second derivative test.