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# the derivative

Posted 11 years ago
 1.The volume of a circular cone is V =  (1/3)?r²h, where r is the radius of the base and h is the height.a. What is the rate of change of the volume with respect to the height if the radius is constant?b. What is the rate of change of the volume with respect to the radius if the height is constant?2.Marginal Cost Functions     The weekly total cost incurred by the Electra Electronics Company in producing its Zephyr laser jet printers is given byC(x) = 0.000002x3  0.02x2 +1000x + 120000    dollars, where x stands for the number of units produced.    a. Find the marginal cost function C and the marginal average        cost function ?.    b. Compute ?(5000), and interpret your results
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Posted 11 years ago
 (* Clear memory *) Clear["Global`*"];  (* Problem 1 *) (* Formula for volume. *) v[r_, h_] := (1/3) \[Pi] r^2 h; (* Rate of change of volume w.r.t height *) D[ v[r,h], h] (* Rate of change of volume w.r.t radius *)D[ v[r,h], r](* Problem 2 *)(* Formula for cost. *)c[x_] :=  0.000002x^3 - 0.02x^2 +1000x + 120000;(* Derivative C'(x) *)D[ c[x], x](* Marginal Average Cost function, MAC = (\[DifferentialD]/\[DifferentialD]x)( c (x)/x ) *)MAC = D[ c[x]/x, x](* Compute MAC(5000) *)MAC /. x -> 5000
Posted 11 years ago
 Of course the posting by Isaac answers your question.  But was the original posting about Mathematica?  It seems more like asking for help solving a homework assignment....  ;-)