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The total cost C(x) in rupees, associate...

The total cost C(x) in rupees, associated with the production of x units of an item is given by `C(x)=0.05x^(3)-0.01x^(2)+20x+1000`. Find the marginal cost when 3 units are produced .

Text Solution

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`C(x)=0.05x^(3)-0.01x^(2)+20x+1000`
Marginal cost = Instantaneous rate of change of total cost at level of output
`=((d(0.05x^(3)-0.01x^(2)+20x+1000))/(dx))_((x=3))`
`=(0.015x^(2)-0.02x+20)_(x=3)`
`=0.15 xx 3^(2)-0.02 xx 3+20`
`=1.35 -0.06 +20`
`=21.35-0.06`
=Rs. 21.29
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The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x)=0. 005 x^3-0. 02 x^2+30 x+5000 . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x)=0. 005 x^3-0. 02 x^2+30 x+5000 . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Knowledge Check

  • If the total cost of producing x units of a commodity is given by C(x)=(1)/(3)x^(2)+x^(2)-15x+300 , then the marginal cost when x=5 is

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  • If C(x) = 3x^(2) - 2x + 3 , the marginal cost when x = 3 is

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    24
    B
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    D
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