Question

100 POINTS!

PLEASE PROVIDE STEPS.

Answer 1

The minimum is x = 3.

Explanation:

C(x) = 100 + 30x + (270/x)

A) C'(x) = 30 − (270/x²)

0 = 30 − (270/x²)

270/x² = 30

x² = 9

x = -3 or 3

B) The production level per day is represented by x, so it is a positive number. X equals 3.

Answer 2

Explanation:

C(x) = 100 + 30x + (270/x)

A) C'(x) = 30 − (270/x²)

0 = 30 − (270/x²)

270/x² = 30

x² = 9

x = -3 or 3

B) x represents the production level per day, so it must be a positive number.

C) If you wish to use first derivative test, show that C'(x) changes signs around x = 3 from negative to positive, thus making x = 3 a minimum.

C'(2) = -37.5

C'(4) = 13.125

Therefore, x = 3 is a minimum.

If you wish to use second derivative test, show that C"(x) is positive at x = 3, thus making x = 3 a minimum.

C"(x) = 540/x³

C"(3) = 20

Therefore, x = 3 is a minimum.