BC What to Do List - AP Calculus Final Review Sheet When you see the words 1 Find the zeros 2 Find equation of the line tangent to f x at(a b 3 Find

# BC What to Do List - AP Calculus Final Review Sheet When...

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AP Calculus – Final Review Sheet When you see the words …. This is what you think of doing 1. Find the zeros 2. Find equation of the line tangent to ( ) x f at ( ) b a , 3. Find equation of the line normal to ( ) x f at ( ) b a , 4. Show that ( ) x f is even 5. Show that ( ) x f is odd 6. Find the interval where ( ) x f is increasing 7. Find interval where the slope of ( ) x f is increasing 8. Find the minimum value of a function 9. Find the minimum slope of a function 10. Find critical values 11. Find inflection points 12. Show that ( ) x f a x lim exists 13. Show that ( ) x f is continuous 14. Find vertical asymptotes of ( ) x f 15. Find horizontal asymptotes of ( ) x f
16. Find the average rate of change of ( ) x f on [ ] b a , 17. Find instantaneous rate of change of ( ) x f at a 18. Find the average value of ( )xfon []ba, 19. Find the absolute maximum of ( ) x f on [ ] b a , 20. Show that a piecewise function is differentiable at the point a where the function rule splits 21. Given ( ) t s (position function), find ( ) t v 22. Given ( ) t v , find how far a particle travels on [ ] b a , 23. Find the average velocity of a particle on []ba, 24. Given ( ) t v , determine if a particle is speeding up at t = k 25. Given ( ) t v and ( ) 0 s , find ( ) t s 26. Show that Rolle’s Theorem holds on [ ] b a , 27. Show that Mean Value Theorem holds on [ ] b a , 28. Find domain of ( ) x f 29. Find range of ( ) x f on [ ] b a , 30. Find range of ( ) x f on ( ) - , 31. Find ( ) x f by definition 32. Find derivative of inverse to ( ) x f at a x =
33. y is increasing proportionally to y 34. Find the line c x = that divides the area under ( ) x f on [ ] b a , to two equal areas 35. ( ) = dt t f dx d x a 36. d dx f t () a u dt 37. The rate of change of population is … 38. The line b mx y + = is tangent to ( ) x f at ( ) b a , 39. Find area using left Riemann sums 40. Find area using right Riemann sums 41. Find area using midpoint rectangles 42. Find area using trapezoids 43. Solve the differential equation … 44. Meaning of ( ) dt t f x a 45. Given a base, cross sections perpendicular to the x -axis are squares 46. Find where the tangent line to ( ) x f is horizontal 47. Find where the tangent line to ( ) x f is vertical 48. Find the minimum acceleration given ( ) t v 49. Approximate the value of ( ) 1 . 0 f by using the tangent line to f at 0 = x
50. Given the value of ( ) a f and the fact that the anti- derivative of f is F , find ( ) b F 51. Find the derivative of ( ) ( ) x g f 52. Given ( ) dx x f b a , find ( ) [ ] dx k x f b a + 53. Given a picture of ( ) x f , find where ( ) x f is increasing 54. Given ( ) t v and ( ) 0 s , find the greatest distance from the origin of a particle on [ ] b a , 55. Given a water tank with g gallons initially being filled at the rate of ( ) t F gallons/min and emptied at the rate of ( ) t E gallons/min on [ ] 2 1 , t t , find a) the amount of water in the tank at m minutes 56. b) the rate the water amount is changing at m 57. c) the time when the water is at a minimum 58. Given a chart of x and ( ) x f on selected values between a and b , estimate ( ) c f where c is between a and b.