Please help on this calculus problem thanks.
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Please help on this calculus problem thanks.

[From: ] [author: ] [Date: 12-11-24] [Hit: ]
c(x) = 0.c(20) = $3,......
If the marginal cost of producing x units of a commodity is given by C'(x)= 0.3x^2+2x and fixed costs are $2000. Find c(x) and the cost of producing 20 units.

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To find c(x) we need to antidifferentiate C'(x)= 0.3x^2+2x. When we do we get:

c(x) = 0.1x^3 + x^2 + k, where k is a constant

We know that k = 2000 because we are told $2000 is the fixed cost. We now have the cost function:

c(x) = 0.1x^3 + x^2 + 2000

The cost of producing 20 units is:

c(20) = $3,200

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yesss
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