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?

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A:

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A: please see the attachment

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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.