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October 23rd, 2013, 04:46 PM   #1
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Derivatives: Exponential Function

The average cost of producing q units of a product is given by
C average=(860/q)+4100(e^((3q+3)/860)/q)
Find the marginal cost if q=101 .
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October 24th, 2013, 01:40 AM   #2
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Re: Derivatives: Exponential Function

marginal cost = dC/dq = -860/q^2 + (4100/860)*(-3/q^2)*(e^((3q+3)/860)/q)
Let substitute 101 for q.
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October 24th, 2013, 02:19 AM   #3
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Re: Derivatives: Exponential Function

marginal cost is the change in the total cost that arises when the quantity produced changes by one unit.

Firstly
(3q+3)/860)/q = (3q+3)/(860q)

If f(q)=(3q+3)/(860q)
then
f'(q) = [(860q)(3) - 860(3q+3)] /[860^2 * q^2] using the quotient rule
=[3q - (3q+3)] /[860 * q*q]
= -3 / (860qq)

C average= 860*q^(-1) + 4100e^[(3q+3)/860q]

dC/dq = (-860 /q^2) + 4100 * [ -3 / (860qq) ] e^[(3q+3)/860q]

When q=101

dC/dq = (-1/10201)[(860 + 14.3023255 e ^ (306 / 86860)]

= -0.086

This doesn't sound right. It would ususally be a positive answer.
It can be negative it just would rarely be.
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