Question

Find the minimum value of the average cost for the given cost function on the given intervals. Upper C (x )equals x cubed plus 33 x plus 432 a. 1 less than or equals x less than or equals 10 b. 10 less than or equals x less than or equals 20

Answer 1

Step-by-step explanation:

C(x) = x^3 + 33x + 432

average cost, Ca = C(x)/x

Ca = x^2 + 33 + 432/x

To find the minimum, we look at the critical numbers

differentiation C(x) = 2x - 432/x^2 = 0

multiplying by x^2

2x^3 - 432 = 0

x =6

x lies in the interval [1, 10}