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REVIEW TEST 2

REVIEW TEST 2. 1. Find the derivative for y = 3x 2 + 5x - 7. A. y’ = 3x + 5. C. y’ = 6x. C. y’ = 6x + 5. D. y’ = 6x + 5 - 7. E. None of the above. No that answer is incorrect. . You need to use the power rule on each of the terms of the equation. The power rule is –

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REVIEW TEST 2

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  1. REVIEWTEST 2

  2. 1. Find the derivative fory = 3x 2 + 5x - 7 A. y’ = 3x + 5 C. y’ = 6x C. y’ = 6x + 5 D. y’ = 6x + 5 - 7 E. None of the above

  3. No that answer is incorrect. You need to use the power rule on each of the terms of the equation. The power rule is – If y = x n , then y’ = n x n – 1 . Please click here to try again.

  4. Yes, the answer is y’ = 6x + 5 Good work on using the power rule! If y = x n , then y’ = n x n – 1 . Please click here for the next question.

  5. 2. Find the derivative fory = 2x – 1 – x – 3 A. y’ = - 2x 0 + 3x – 2 • y’ = -2x – 2 – 3x – 4 C. y’ = 2x – 2 + 3x – 4 D. y’ = - 2x – 2 + 3x – 4 E. None of the above

  6. No that answer is incorrect. You need to use the power rule on each of the terms of the equation. The power rule is – If y = x n , then y’ = n x n – 1 . Watch your negative signs! Please click here to try again.

  7. Yes, the answer is y’ = - 2x – 2 + 3x – 4 Good work on using the power rule! If y = x n , then y’ = n x n – 1 . Please click here for the next question.

  8. 3. Find the derivative fory = (2x 2 – x + 1)(x – 2) A. y’ = (4x – 1)(1) • y’ = 6x 2 - 10x + 3 C. y’ = (2x 2 – x + 1)(1) + (x – 2)(4x – 1) D. y’ = (4x – 1)(x - 1) E. None of the above

  9. Too bad that answer is incorrect. You need to use the product rule. The product rule is – If f (x) = F (x) • S (x), Then f ’ (x) = F (x) • S’ (x) + S (x) • F ’(x) Please click here to try again.

  10. Yes, the answer is y’ = 6x 2 - 10x + 3 or y’ = (2x 2 – x + 1)(1) + (x – 2)(4x – 1) Good work on using the product rule If y = f · s , then y’ = f · s’ + s · f’ . Please click here for the next question.

  11. 4. Find the derivative for A. B. C. D. y’ = (5x + 2)(2x) – (x 2 + 3) (5) E. None of the above

  12. Sorry, that answer is incorrect. You need to use the quotient rule. The quotient rule is – If Then Please click here to try again.

  13. Great, the correct answer is OR You used the quotient rule correctly!! If then Please click here for the next question.

  14. 5. Find the derivative for A. y’ = - 2 x 1/2 B. y’ = 4 x – 3/2 D. y’ = 4 x 1/2 C. y’ = - 2 x – 3/2 E. None of the above

  15. Not quite, that answer is incorrect. Change the equation to remove the radical to – y = 4x – 1/2 and use the power rule. Please click here to try again.

  16. Hey great, the correct answer is y’ = - 2 x – 3/2 Nice work on the power rule and negative exponents. Please click here for the next question.

  17. 6. Find the derivative for y = (x 2 – 3x + 6) 5 A. y’ = 5 (x 2 – 3x + 6) 4 B. y’ = (x 2 – 3x + 6) 5 (2x – 3) C. y’ = (2x - 3) 5 D. y’ = 5 (x 2 – 3x + 6) 4 (2x – 3) E. None of the above

  18. Too bad, that answer is incorrect. You need to use the chain rule with u = x 2 – 3x + 6 Please click here to try again.

  19. OK, the correct answer is y’ = 5 (x 2 – 3x + 6) 4 (2x – 3) Good use of the chain rule with u = x 2 – 3x + 6 !! Please click here for the next question.

  20. 7. Find the derivative for A. y’ = x (x 2 + 3) – 1/2 B. y’ = (x 2 + 3) – 1/2 C. D. y’ = 1/2 (x 2 + 3) - ½ (2x) E. None of the above

  21. Too bad, that answer is incorrect. You need to rewrite the equation without a radical and then use the chain rule y = (x 2 + 3) ½ and the let u = x 2 + 3 Please click here to try again.

  22. Terrrrriffffic!! Rewrite the equation without a radical and then use the chain rule - y = (x 2 + 3) ½ and the let u = x 2 + 3 Then y’ = x (x 2 + 3) – ½ OR y’ = 1/2 (x 2 + 3) - ½ (2x) OR Please click here for the next question.

  23. 6. If f (x) = 2x 3 - 3x 2 – 5x + 3, find the second derivative. A. y” = 6x– 6 B. y” = 6x 2 C. y” = 12x - 6 D. y” = 6x 2 - 6x - 5 E. None of the above

  24. No that answer is incorrect. You need to take the derivative of the derivative! Please click here to try again.

  25. Yes Yes Yes, the correct answer is y” = 12x - 6. y’ = 6x 2 - 6x – 5 and y” = 12x - 6 Please click here for the next question.

  26. APPLICATIONS Now, let’s try some application problems

  27. 9. A drug is injected into the bloodstream. The concentration of the drug after x hours is given by A. Find the marginal concentration after 3 hours (4 decimal places). for 0  x  10. A. C’ (x) = 0.0462 ml/cm 3 B. C’ (x) = – 0.1746 ml/cm 3 C. C’ (x) = – 0.0059 ml/cm 3 D. C’ (x) = 0.5428 ml/cm 3 E. None of the above

  28. Sorry that answer is incorrect. To find the marginal concentration graph the given function and under the CALC menu use the dy/dx choice at x = 3. Please click here to try again.

  29. Yes, the answer is C’ (x) = – 0.0059 ml/cm 3 from your graphing calculator. NOTE: You will need this answer for the next question. Please click here for the next question.

  30. 10. A drug is injected into the bloodstream. The concentration of the drug after x hours is given by B. Interpret the results of the previous question. for 0  x  10. Take a minute and try to write a response. Go to a representative correct answer.

  31. The drug concentration after three hours is decreasing by about 0.0059 ml/cm 3 for the next hour. Please click here for the next question.

  32. 11. The total profit from the sale of text books is P (x) = 30 x – 0.3 x 2 - 200 0 ≤ x ≤ 100.A. Find the marginal profit when x = 40. A. P’ (x) = 0 B. P’ (x) = – 6 C. P’ (x) = 6 D. P’ (x) = undefined E. None of the above 32

  33. Oooooh too bad that answer is incorrect. To find the marginal profit consider graphing the function and under the CALC menu use the dy/dx choice at x = 40. Please click here to try again. 33

  34. Yes, the answer is P’ (x) = 6 from your graphing calculator. NOTE: You will need this answer for the next question. Please click here for the next question. 34

  35. 12. B. The total profit from the sale of text books is P (x) = 30 x – 0.3 x 2 - 200 0 ≤ x ≤ 100.B. Interpret P ‘ (40) = 6 Write an interpretation and then click here to see a representative answer. 35

  36. The profit when selling the next textbook (#41) will increasing by about $6. Please click here for the next question. 36

  37. 13. The total profit (in dollars) from the sale of x calculators is P (x) = 22x – 0.2x 2 – 400 A. Find the average profit per calculator if 50 calculators are produced and sold. for 0  x  100. A. P (x) = $4 • P (x) = $3 C. P (x) = $3.50 D. P (x) = $2 E. None of the above

  38. Too bad that answer is incorrect. The average profit is the profit divided by x. Calculate the profit at 50 and divide by 50. If you wish you can graph the average profit on your calculator and find CALC then VALUE at x = 50. Please click here to try again.

  39. Yes, the answer is OR Please click here for the next question.

  40. 14. The total profit (in dollars) from the sale of x calculators is P (x) = 22x – 0.2x 2 – 400 B. Find the marginal average profit at a production level of 50 calculators. for 0  x  100. A. P’ (x) = $ 0.04 • P’ (x) = $ - 0.04 C. P’ (x) = $ 0.40 D. P’ (x) = $ - 0.40 E. None of the above

  41. No that answer is incorrect. There are several ways to get the marginal average profit. Perhaps the easies is to graph the average profit and go to CALC and dy/dx at 50. Please click here to try again.

  42. Yesaroonie, the answer is – 0.04. NOTE: You will need this answer for the next question. Please click here for the next question.

  43. 15. Write a brief interpretation of the results of the previous problem. Take a minute and write an interpretation. Go to a representative correct answer.

  44. The average profit is decreasing by about $0.04 for the sale of the 51st calculator. Please click here for the next question.

  45. 16. The price-demand and cost equations for producing gadgets are given by: p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0  x  6,000.A. Find the revenue function. A. R (x) = x (6000 - x)/30 • R (x) = (6000 - x)/(30x) C. R (x) = x (72000 + 60x) D. R (x) = p (x) + C (x) E. None of the above

  46. Sorry that answer is incorrect. To find the revenue function use R (x) = xp, where p is the price-demand function. Please click here to try again.

  47. You have what it takes. The correct answer is R (x) = xp = x (6000 - x)/30 NOTE: You will need this answer for the next question. Please click here for the next question.

  48. 17. The price-demand and cost equations for producing gadgets are given by: p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0  x  6,000.A. Find the marginal revenue function. A. R’ (x) = 60000 – x/30 • R’ (x) = p’ (x) – C’ (x) C. R’ (x) = 200 – x/15 D. R’ (x) = 200 – x/30 E. None of the above

  49. Not the correct answer. To find the marginal revenue function you need to find the derivative of the revenue function from the previous problem. R (x) = x (6000 - x)/30 Please click here to try again.

  50. Great calculus work. The correct answer is the derivative of R (x) = x (6000 - x)/30 R (x) = x (6000 - x)/30 = 200x – x 2/30 and R’ (x) = 200 – 2x/30 = 200 – x/15 NOTE: You will need this answer for the next question. Please click here for the next question.

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