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S1 Final Review: Speed Trials

0 15 45 30. 3 min. S1 Final Review: Speed Trials. You should be averaging 3 minutes per multiple choice question. If f(u) = ln u and g(u) = e 3u , the g(f(1)). Stop. 0 15 45 30. 1. Given y = √x 3 , what is y “‘(4)?. Stop. 0 15 45 30. 2. Given Then f “‘ (x)=. 0

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S1 Final Review: Speed Trials

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  1. 0 15 45 30 3 min S1 Final Review: Speed Trials You should be averaging 3 minutes per multiple choice question

  2. If f(u) = ln u and g(u) = e3u, the g(f(1)) Stop 0 15 45 30 1

  3. Given y = √x3, what is y “‘(4)? Stop 0 15 45 30 2

  4. Given Then f “‘ (x)= 0 15 45 30 Stop 3

  5. 0 15 45 30 Stop 4

  6. A restaurant realizes a monthly revenue of R(x) = 1000x – 10 x2 dollars per month when the fee per person is x dollars. What is the marginal revenue when the fee is $15 per person? 0 15 45 30 Stop Marginal Cost = Derivative 5

  7. 0 15 45 30 Stop Plug in 5, get 0/0 L’Hopital or Factor 6

  8. If y = vlnu and u and v are both differentiable, then uy’ is 0 15 45 30 Stop 7

  9. If y = 5 * 22x + 1 then y’ = 0 15 45 30 Stop 8

  10. If f(x) = ex – 1 sin x – 1, then f ‘(1) = 0 15 45 30 Stop 9

  11. Which of the following statements is (are) false for f(x) = ln(x + 1)sinx + 1 0 15 45 30 Stop 10

  12. If x cos y = x + y then what is dy/dx 0 15 45 30 Stop 11

  13. 0 15 45 30 Stop Recognize definition of derivative f (a + h) = 2e2+h f (a) = 2e2 a = 2 f (x) = 2ex f ‘(x) = 2ex f ‘(x) = 2e2 12

  14. Suppose a particle moves on a straight line with a position function of s(t) = –2t2 + 8t. In what interval of time is the particle speeding up? 0 15 45 30 Stop v = –4t + 8 = –4(t – 2) v = 0 @ t = 2 v > 0 when t < 2 v < 0 when t > 2 a = –4 < 0 always Speeding up when a & v same sign 13

  15. The tangent line to the graph of m(x) at the point (2, 7) has slope of –4. Use the equation of the tangent to estimate m(2.02) 0 15 45 30 Stop 14

  16. Water flows into a cylindrical tank at a constant rate of 4 cubic meters per second. The radius of the cylinder is 5 meters. At what rate is the water level rising? 0 15 45 30 Stop 15

  17. If the position of a particle at any time t is given by s = –t3 – 5t, then the speed of the particle at time t = 7 is 0 15 45 30 Stop 16

  18. How many inflection points does 3x4 – 5x3 – 9x + 2 have? 0 15 45 30 Stop 17

  19. The circumference of a circle is changing at a rate of 10 cm/sec. At what rate is the radius of the circle changing when the diameter is 5 cm? 0 15 45 30 Stop 18

  20. 0 15 45 30 Stop Recognize definition of derivative f (a + h) = sin(π + h) f (a) = sin(π) a = π f (x) = sin x f ‘(x) = cos x f ‘(π) = cos π 19

  21. 0 15 45 30 1 min S1 Final Review: Speed Trials Some questions you might need a minute to think, so to average out there should be conceptual questions you should be able to answer instantly (under 1 minute)

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