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

Question

Manuel Esparza

Business

18 July, 22:42

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

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Murillo · Answer 1

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}