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(b) The result f ro does dA/dr represent geometrically? (c) U se the difference

ID: 2895560 • Letter: #

Question

(b) The result f ro does dA/dr represent geometrically? (c) U se the difference quotient to explain the observa- tion you made in part (b). 58. Suppose W is proportional to r3. The derivative dW/dr , 59. Show that for any power function f(x) = xn, we have 60. The cost to produce q items is C(q) = 1000 + 2q2 dol- is proportional to what power of r? lars. Find the marginal cost of producing the 25th item Interpret your answer in terms of costs. 61 The demand curve for a product is given by q=300-3p, where p is the price of the product and q is the quantity that consumers buy at this price. (a) Write the revenue as a function, R(p), of price (b) Find R'(10) and interpret your answer in terms of

Explanation / Answer

60)

Sol:

Given C(q) =1000 +2q^2

The cost at q = 25 is s C(25) = 1000 + 2 * 25^2 = 2250 dollars

he marginal cost is the derivative of the cost, C'(q) = 4q , so at q = 25, C'(25)= 4*25 = 100 dollars per unit.

Therefore, it costs $2250 to make 25 units of this product, and at that level of production costs are increasing at a rate of $100 per unit.