anonymous
  • anonymous
The cost of producing x units of a certain commodity is given by P (x) =1000 + ∫ ^x to 0 MC (s)ds, where P is in dollars and M (x) is marginal cost in dollars per unit. B. Suppose the production schedule is such that the company produces five units each day. That is, the number of units produced is x= 5t, where t is in days, and t = 0 corresponds to the beginning of production. Write an equation for the cost of production P as a function of time t. C. Use your equation for P (t) from part B to find dP/dt . Be sure to indicate units and describe what dP/dt represents.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Where is A.?
anonymous
  • anonymous
\[ P(x) = 1000+\int _0^xMC(s)ds \] B. Just wants you to substitute \(x=5t\). So \[ P(t) = 1000+\int _0^{5t}MC(s)ds \](This is an abuse of notation, we should not be using the same function name here). C. Wants you to use the fundamental theorem of Calculus.
anonymous
  • anonymous
\[ \frac{d}{dx} \int_a^{g(x)}f(t)dt = (f\circ g)(x)\cdot \frac{dg}{dx} = f(g(x))\cdot g'(x) \]

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