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Question 179 of 188

Q.The cost (in rupees) of producing x items in factory, each day is given by 𝐢(π‘₯) = 0.00013π‘₯3 + 0.002 π‘₯2 + 5π‘₯ + 2200 Find the marginal cost when 150 items are produced.

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Marginal cost is Cβ€²(x)C'(x). Here Cβ€²(x)=0.00039x2+0.004x+5C'(x) = 0.00039x^2 + 0.004x + 5, and at x=150x = 150 this equals ₹ 14.375\mathbf{\text{β‚Ή}\,14.375} per item.

Marginal cost is the derivative of the total cost function. Given

C(x)=0.00013x3+0.002x2+5x+2200,C(x) = 0.00013x^3 + 0.002x^2 + 5x + 2200,

differentiate term by term:

Cβ€²(x)=3(0.00013)x2+2(0.002)x+5=0.00039x2+0.004x+5.C'(x) = 3(0.00013)x^2 + 2(0.002)x + 5 = 0.00039x^2 + 0.004x + 5. …

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