The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 41x − 0.04×2. (a) Find the marginal cost function C'(x). C'(x) = ___________ Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ ________ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ _____ per teddy bear. The exact cost of producing the 101st teddy bear is $ ________ . Thus, there is a difference of $ ___________ .

The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula

C(x) = 100 + 41x − 0.04x^{2}.

(a) Find the marginal cost function C’(x).

C'(x) = ___________

Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears.

$ ________ per teddy bear

Compare this with the exact cost of producing the 101^{st} teddy bear (in $).

The cost is increasing at a rate of $ _____ per teddy bear. The exact cost of producing the 101^{st} teddy bear is $ ________ . Thus, there is a difference of $ ___________ .

(b)Find the average cost function C, and evaluate C(100) (in $).

C(x)= _______

C(100) = $ ______ per teddy bear

What does the answer tell you?

The average cost of producing the first hundred teddy bears is $ _________ per teddy bear.

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