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# (a) Suppose that a company's total cost (TC) of producing x thousand units of output is given by the function TC= 2X^3+5 . Find the derivative of...

(a) Suppose that a company's total cost (TC) of producing x thousand units of output is given by the function TC= 2X^3+5 . Find the derivative of this function. Why does it give the marginal cost (MC) of production? (MC= 6X^2)

(b) The output in (a) is sold according to the demand equation p= 50 - 0.5X , where p is the price per unit. Find the total revenue (TR) function, where TR is price times quantity sold. Calculate the derivative of the TR function. Why does it give the marginal revenue (MR)? For this question, do i need to multiply 50 - 0.5X by X or multiply 50- 0.5X by 6X^2?

(c) Find the positive output x (rounded to 3 decimal places) at which MR=MC.