Question

The cost function C(x), in rupees, of producing x items (x ≥ 15) in a certain factory is given by $straight C left parenthesis straight x right parenthesis space equals space 20 plus 10 straight x squared plus 15 over straight x.$ Determine the marginal cost function and the marginal cost of producing 100 items.

Solution

Here, $straight C left parenthesis straight x right parenthesis space equals space 20 plus 10 straight x squared plus 15 over straight x space space space space rightwards double arrow space space space space space space straight C space equals space 20 plus 10 straight x squared plus 15 straight x to the power of negative 1 end exponent$
Marginal cost function $equals space dC over dx space equals space 0 plus 20 straight x minus 15 straight x to the power of negative 2 end exponent space equals space 20 straight x minus space 15 over straight x squared$
When x = 100, marginal cost = 20 (100) - $fraction numerator 15 over denominator left parenthesis 100 right parenthesis squared end fraction$
$equals space 2000 minus 15 over 10000 space equals space left parenthesis 2000 minus.001 right parenthesis space nearly space equals space Rs. space 2000 space nearly.$

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Application Of Derivatives

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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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