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Calculus
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  1. Find the cost function if the marginal cost function is given by C'(x) = x^(2/5) + 9
  2. Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is R'(x) = .03x^2 - .07x + 208
May 7th, 2015

1. Marginal cost function C'(x)= (1/5) x^2 + 9 
Cost function C(x) = (1/5) ∫ (x^2+9) dx 

= (1/5) ∫ x^2 dx + 9 ∫ dx = (1/5)(1/3) x^3 + 9x + C 
C(x) = (1/15) x^3 + 9x + C 

2. dR/dx = .03x^2 - .07x + 208

integrate with respect to x
R=0.01x^3-0.035x^2+208x
since revenue = price * quantity 
factor a x
r = x(0.01x^2-0.035x+208) + constant/q 
r = q * p 

p = 0.01x^2-0.035x+208 + constant/q


May 7th, 2015

Hello and thank you for your reply. However, the first question was incorrect, for whatever reason. The second question was reset to a different one due to a timeout, I apologize. If you could rework them I would be very grateful..

  1. Find the cost function if the marginal cost function is given by C'(x) = x^(2/5) + 9
  2. Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is R'(x) = .09x^2 - .08x + 168

May 7th, 2015

The first question has not changed, but the second has. When inputting the first answer, it was not accepted as correct.

May 7th, 2015

1. C(x)=5/7 x^(7/5) +9x +C

2. 0.03x^3-0.04x^2+168x+C

May 7th, 2015

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