# Assume that it costs a company approximately. C(x) = 400,000 + 160x + 0.003x2dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 160+.006x   Use it to estimate how fast the cost is increasing when x = 10,000.\$   per smartphoneCompare this with the exact cost of producing the 10,001st smartphone.The cost is increasing at a rate of \$   per smartphone. The exact cost of producing the 10,001st smartphone is \$   . Thus, there is a difference of \$   . (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x)=    C(10,000)= \$

Question
Assume that it costs a company approximately.

C(x) = 400,000 + 160x + 0.003x2
dollars to manufacture x smartphones in an hour.

(a) Find the marginal cost function.

160+.006x

Use it to estimate how fast the cost is increasing when x = 10,000.
\$   per smartphone
Compare this with the exact cost of producing the 10,001st smartphone.
The cost is increasing at a rate of \$   per smartphone. The exact cost of producing the 10,001st smartphone is \$   . Thus, there is a difference of \$   .

(b) Find the average cost function C and the average cost to produce the first 10,000 smartphones.

C(x)=

C(10,000)
= \$
check_circle

Step 1

C'(x)= 160+.006x

C'(10000)=160+.006(10000)=220

Answer: The cost is increasing by \$220 per smart phone when x = 10,000.

Step 2

To find exact cost of 10,001 smartphone, we plug x=10001 in C(x).

The cost is increasing at a rate of \$ 220  per smartphone. The exact cost of producing the 10,001st smartphone is \$ 2300220  . Thus, there is a difference of \$ 220  .

Step 3

Average cost function c(x)= C(x)/x help_outlineImage TranscriptioncloseС() с (x)%3D х 400,000+160х+0.003x? с(х)- 0.003x 160х 400000 с(х)- X х 400000 с(х)- .+160+0.003х X fullscreen

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