My Math Forum Cost function

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 November 25th, 2011, 11:55 AM #1 Newbie   Joined: Oct 2011 Posts: 26 Thanks: 0 Cost function The marginal cost for a product is MC=40 + x^2. Find the cost function if the cost for 6 units is \$500. I'm not sure exactly what to do with this one. I would think that you simply find the integral of MC to get the cost function, but the 6 units for 500 leads me to belive that's not so. What do i do?
 November 25th, 2011, 01:15 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Cost function We are essentially given the initial value problem: $\frac{dC}{dx}=40+x^2$ where $C(6)=500$ Thus, we may write: $\int_{500}\,^{C(x)}\,dC=\int_6\,^x 40+x^2\,dx$ $C(x)-500=$40x+\frac{x^3}{3}$_6^x=$$40x+\frac{x^3}{3}$$-$$40\cdot6+\frac{6^3}{3}$$=40x+\frac{x^3}{3}-312$ $C(x)=40x+\frac{x^3}{3}+188$

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