Question

Designers want to introduce a new line of bookcases. They want to make at least 100 bookcases, but not more than 2000 of them. They predict the cost of producing x bookcases is ?(?). Assume that ?(?) is a differentiable function. Which of the following must they do to find the minimum average cost, ?(?)=?(?)/x

(1) find the points where ?′(?)=0 and evaluate ?(?) there

(2) compute ?″(?) to check which of the critical points in (I) are local maxima

(3) check the values of ? at the endpoints of its domain.

A group of designers wants to introduce a new line of bookcases. They want to make at least 100 bookcases, but not more than 2000 of them. They predict the cost of producing ?x bookcases is ?(?)C(x). Assume that ?(?)C(x) is a differentiable function. Which of the following must they do to find the minimum average cost, ?(?)=?(?)?A(x)=C(x)x?

(1) find the points where ?′(?)=0A′(x)=0 and evaluate ?(?)A(x) there

(2) compute ?″(?)A″(x) to check which of the critical points in (I) are local maxima

(3) check the values of ?A at the endpoints of its domain.

(a) 1 only

(b) 1 and 2 only

(c) 1 and 3 only

(d) 1, 2, and 3.

Answer 1

To find the minimum average cost, we need to find the value of x which results in minimum value of A(x)

A function is maximum or minimum when it flattens (slope is zero).

For this we find the derivative of A(x) which is A'(x) and evaluate by putting A'(x) = 0.

For further evaluation we find A''(x) and eliminate the critical points found earlier which are a local maxima. This leaves us with local minima.

Thus correct option is (b) 1 and 2 only

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