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Question
Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
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Solution
Total cost, C = 10e2x
Marginal cost = `("dC")/("d"x)`
= `"d"/"dx"(10"e"^(2x)) = 10"d"/"dx"("e"^(2x))`
= `10*"e"^(2x)*"d"/("d"x)(2x) = 10*"e"^(2x)*2(1)`
= 20e2x
When x = 2,
Marginal cost =`(("dC")/("dx"))_(x = 2)` = 20e4
Average cost = `"C"/x` = `(10"e"^(2x))/x`
When x = 2 average cost = `(10e^4)/2` = 5e4
∴ When x = 2, marginal cost is 20e4 and average cost is 5e4.
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