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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. - Mathematics and Statistics

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प्रश्न

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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उत्तर

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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Rules of Differentiation (Without Proof)
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differentiation - Exercise 9.2 [पृष्ठ १२३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 11 Maharashtra State Board
पाठ 9 Differentiation
Exercise 9.2 | Q II. (8) | पृष्ठ १२३

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