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

C(x) = 100 +35x0.02x².

(a)Find the marginal cost functionC'(x).

C'(x) =

350.04x

Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears.$ per teddy bearCompare this with the exact cost of producing the 101^stteddy bear (in $).The cost is increasing at a rate of $ per teddy bear. The exact cost of producing the 101^stteddy bear is$ .Thus, there is a difference of $ Outstanding!.(b)Find the average cost function

C,

and evaluate

C(100)

(in $).

C(x)

=

100x+350.02x

C(100)

= $ per teddy bearWhat does the answer tell you?The average cost of producing the first hundred teddy bears is $ per teddy bear.