1 / 134

REVIEW TEST 3

REVIEW TEST 3. 1. Let’s begin Next Slide with a few practice derivatives. To skip practice derivative and go to implicit derivatives click here . Please click “ON THE LETTER” of the correct answer!. 2. 1. Find the derivative for y = 3x 2 + 5x - 7. A. y’ = 3x + 5. C. y’ = 6x.

kanoa
Download Presentation

REVIEW TEST 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. REVIEWTEST 3 1

  2. Let’s begin Next Slidewith a few practice derivatives.To skip practice derivative and go to implicit derivatives click here.Please click “ON THE LETTER” of the correct answer! 2

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 4. Find the derivative for A. B. C. D. y’ = (5x + 2)(2x) – (x 2 + 3) (5) E. None of the above 12

  13. 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

  14. Great, the correct answer is OR You used the quotient rule correctly!! If then Please click here for the next question. 14

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 8. Implicitly differentiate to find y’ if 0 = 3x 2 – y + 4 A. y’ = - 6x • y’ = 6x C. y’ = 6x - y D. y’ = 6x - x E. None of the above

  25. Sorry that answer is incorrect. To implicit differentiate remember to take the derivative of each term of the function with respect to x. If 0 = 3x 2 – y + 4 then d/dx (0) = d/dx (3x 2 ) – d/dx (y) + d/dy (4) Please click here to try again.

  26. Yes, the answer is y’ = 6x. d/dx (0) = d/dx (3x 2 ) – d/dx (y) + d/dy (4) 0 = 6x - y’ + 0 so y’ = 6x Please click here for the next question.

  27. 9. Implicitly differentiate to find y’ if0 = x 2 + y 2 + x + y + 3 A. B. C. D. E. None of the above

  28. No that answer is incorrect. To implicit differentiate remember to take the derivative of each term of the function with respect to x. If 0 = x 2 + y 2 + x + y + 3 then d/dx (0) = d/dx (x 2 ) + d/dx (y 2 ) + d/dx (x) + d/dx (y) + d/dx (3) Now finish the derivatives!! Please click here to try again.

  29. Yes indeeeedy, the answer is If 0 = x 2 + y 2 + x + y + 3 then d/dx (0) = d/dx (x 2 ) + d/dx (y 2 ) + d/dx (x) + d/dx (y) + d/dx (3) 0 = 2 x + 2 y y’ + 1 + y’ + 0 and solving for y’ yields Please click here for the next question.

  30. 10. Implicitly differentiate to find y’ if x ln y + 2y = 2x 3Please click on the letter and not the equation. A. B. C. D. E. None of the above

  31. Too bad that answer is incorrect. This one is difficult!! To implicit differentiate remember to take the derivative of each term of the function with respect to x. This problem also involves the product rule!!! If x ln y + 2y = 2x 3 then d/dx (x ln y) + d/dx (2y ) = d/dx (2x 3 ) Now finish the derivatives!! You need the product rule here. Please click here to try again.

  32. Yes, the answer is If x ln y + 2y = 2x 3 then d/dx (x ln y) + d/dx (2y ) = d/dx (2x 3 ) x (1/y) y’ + ln y (1) + 2 y’ = 6x 2 and solving for y’ yields Please click here for the next question.

  33. 11. How much would a $2,000 investment be worth in 12 years at 9% compounded continuously? A. $5,865.67 • $5,889.36 D. $5,885.36 C. $5,885.67 E. None of the above

  34. Sorry, that answer is incorrect. Remember that the continuous compound interest formula is – And you have all the information except for A. Please click here to try again.

  35. Great, the correct answer is $5,889.36, since Please click here for the next question.

  36. 12. How much would you need to invest at 11% compounded continuously for 8 years to end up with $5,000? A. $2,082.25 B. $2,082.91 D. $2,073.25 C. $2,073.91 E. None of the above

  37. Not quite, that answer is incorrect. Remember that the continuous compound interest formula is – And you have all the information except for P. Please click here to try again.

  38. Hey great, the correct answer is $2,073.91, since Please click here for the next question.

  39. 13. What continuously compounded interest rate is needed to double your money in 13 years? A. 5.54% B. 2.32% D. 5.33% C. 5.25% E. None of the above

  40. Too bad, that answer is incorrect. Remember that the continuous compound interest formula is – And you have all the information except for r. This will be a solution that needs natural logs. Please click here to try again.

  41. OK, the correct answer is 5.33%, since Remember your money is doubling so A/P = 2 Please click here for the next question.

  42. 14. An automobile depreciates at a rate of 20% per year. How long will it take for the used value to be one-half the new value? A. 3.1 years B. 2 years D. 2.9 years C. 0.9 years E. None of the above

  43. Not quite, that answer is incorrect. Remember that the depreciation formula is – And you have all the information except for t. This will be a solution that needs logs. Please click here to try again.

  44. Terrrrriffffic, the correct answer is 3.1 years, since Please click here for the next question.

  45. 15. How much would a $2,000 investment be worth in 12 years at 9% compounded monthly? A. $5865.67 B. $5,889.36 D. $5,885.36 C. $5,885.67 E. None of the above

  46. Remember that the compound interest formula is – And you have all the information except for A. That answer is incorrect. It is a hard one! Please click here to try again.

  47. Terrrrriffffic, the correct answer is $5865.67, since Please click here for the next question.

  48. 16. How much would you need to invest at 11% compounded quarterly for 8 years to end up with $5,000? A. $2,073.91 B. $2,075.71 D. $2,198.71 C. $2,098.71 E. None of the above

  49. Remember that the compound interest formula is – And you have all the information except for P. That answer is incorrect. Please click here to try again.

  50. Terrrrriffffic, the correct answer is $2,098.71, since Please click here for the next question.

More Related