Suppose the total cost function, in dollars, for the production of x units of a product is given by C(x) = 4000 + 55x + 0.1x2. Then the average cost of producing x items is %3D total cost 4000 + 55 + 0.1x = (x)- (a) Find the instantaneous rate of change of average cost with respect to the number of units produced. That is to say, find C' (x). (b) Find the level of production at which this rate of change equals zero. In other words, solve the equation C' (x) = 0. (c) At the x value found in part (b), find the instantaneous rate of change of cost and find the axerage cost WWhat do you notice?

Q: Suppose the supply of x units of a product at price p dollars per unit is given by p = 20 + 40…

A:

Q: Find Cost Function 314+4 C'(x)=x+4 $ 81 units

A: Given, C'(x) = x34 + 4  and cost of 81 units is  1629

Q: At time 3 seconds an inflatable cylinder has the radius 5 inches and the length 20 inches, that is,…

A: Given that  At time 3 seconds an inflatable cylinder has radius 5 inches and length 20 inches…

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A: A factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula…

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Q: The total cost in dollars to product q items is given by the cost function C(q) = 500 + 3q +q. %3D…

A:

Q: The demand D(s) for a product is the number of consumers who will buy the product at a price of s…

A: a) 50 cents= $ 0.50 So we have to find D(0.50) to find the number of books sold.

Q: f(x)= -2x2 + 3 from x = 2 to x = 5 Average rate of change =

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Q: A 600 gallon tank is initially half full with pure water. A mixture containing a concentration of 1…

A: Let, the volume function be vt

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.