Question

2.If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 24,000 + 290x + 6x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ per unit

3. If C(x) = 16000 + 600x − 1.8x2 + 0.004x3 is the cost function and p(x) = 4200 − 6x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

4.A manufacturer has been selling 1000 flat-screen TVs a week at $300 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week. (a) Find the demand function (price p as a function of units sold x). p(x) = (b) How large a rebate should the company offer the buyer in order to maximize its revenue? $ (c) If its weekly cost function is C(x) = 76,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit? $

5. Find the most general antiderivative of the function. f(x) = (x + 2)(2x − 1) It is not true that if F and G are antiderivatives of f and g, respectively, then F · G is an antiderivative of f · g. Therefore, in order to find the antiderivative of (x + 2)(2x − 1), we must first expand this product, obtaining x2 + 3x − _____________

6. Find the most general f. f ''(x) = 5x + sin(x) To find f(x) given f ''(x), we must first find the antiderivative of f ''(x) to obtain f '(x), and then find the antiderivative of f '(x) to obtain f(x). Since the derivative of cos(x) is , the antiderivative of sin(x) is

7. Find f. f '(t) = 2 cos(t) + sec2(t), −π/2 < t < π/2, f(π/3) = 4

8. Find f. f '(x) = 5/\sqrt{1-x^2} , f(1/2)=3

9. Find f. f ''(t) = 12/ \sqrt{t} , f(4) = 38, f '(4) = 18

10. Find f. f '''(x) = cos(x), f(0) = 7, f '(0) = 8, f ''(0) = 5

11. A particle is moving with the given data. Find the position of the particle. v(t) = 1.5\sqrt{t}, s(4) = 15

12. A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 5t + 3, s(0) = 0, s(1) = 20

13. A stone was dropped off a cliff and hit the ground with a speed of 144 ft/s. What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.) We know that s(t) =at2 + v0t + s0. n this situation, we have a =_____ ft/s2, v0 =__________ft/s, and s0 = h, where h is the height of the cliff (in feet) that we wish to find.

14. A company estimates that the marginal cost (in dollars per item) of producing x items is 1.84 − 0.002x. If the cost of producing one item is $572, find the cost of producing 100 items. The marginal cost function is the derivative of the cost function C(x). So we know that C '(x) = 1.84 − 0.002x. Therefore,C(x) = ________ + K.

15. A car braked with a constant deceleration of 40 ft/s2, producing skid marks measuring 80 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

16. Find f. f ''(x) = 48x2 + 2x + 4, f(1) = 2, f '(1) = −2 17.A particle is moving with the given data. Find the position of the particle. a(t) = t − 10, s(0) = 6, v(0) = 5 18.A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t), s(0) = 3, v(0) = 2

Answer 1

given (cn) = 24000 ta (29) = 24000 +29097621 000 + Dobroeskoue 189736.66 Total cost of produlian ob 1000 wüts CC1000) = 24000 +290 (lood) +6C100032 - 314000 + Beenmodeoco 18 Cclood) = 10002 Kolon 503,736.66. © average cost of soroduction of looo mits 503716166 Ĉciones - CC1000) - 00 Savoce - South 503.73666 ove) Tooo 1000 © Martinal cost c'() = 290 +62 21:24 cla) = 280 +9:22 when produltion is lone .. c'econd) = 280+9 (100oy'n c'curo) = 574.604989 hinimizing average cool @ Chan) - ESTANTES e cas =ČCA) 250+90= 24000 72907621 78079a1 = 24000 +380 +Gava Scanned with CamScanner 3al2 = 24001 -

33= 24000 3 23/2 = 5000 23 - (Somo)? a= (so) / * = 400 at 100 units minimize average costs: mu a a Now mininum average cost Toba eux) = 2uodo fasoa +Gamla COX) = 24000 faso +6912 a at 400 . Ĉ(400) = 2400 +290 +6 (400) = 60+230 +92-951 Ĉ(400) = 442.9516 - minimum averge cost 442.9516 CS$canned with CamScanner