The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x³- 0.02 x²+ 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.

Solution

Here C(x) = 0.005 x³- 0.02 x²+ 30 x + 5000
$therefore space space space space space straight C space equals space 0.005 space straight x cubed minus space space 0.02 space straight x squared space plus space 30 space straight x space plus space 5000$
Marginal cost = $dC over dx space equals space 3 left parenthesis 0.005 right parenthesis space straight x squared minus space 2. space left parenthesis 0.02 right parenthesis space straight x space space plus space 30$
When x = 3, Marginal cost = 3 (0.005) (3)² - 2 (0.02) (3) + 30
= 27(0.005) - 6 (0.02) + 30
=0.0135 - 0.12 + 30 = 30.015 = Rs. 30.02 nearly

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Application Of Derivatives

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x³- 0.02 x²+ 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.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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Application Of Derivatives

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x3 - 0.02 x2 + 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.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x³- 0.02 x²+ 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.