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 ( )xfat ()ba,3. Find equation of the line normal to ( )xfat ()ba,4. Show that ( )xfis even 5. Show that ( )xfis odd 6. Find the interval where ( )xfis increasing 7. Find interval where the slope of ( )xfis 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 ( )xfax→limexists 13. Show that ( )xfis continuous 14. Find vertical asymptotes of ( )xf15. Find horizontal asymptotes of ( )xf
16. Find the average rate of change of ( )xfon ba,17. Find instantaneous rate of change of( )xfat a 18. Find the average value of ( )xfon ba,19. Find the absolute maximum of ( )xfon ba,20. Show that a piecewise function is differentiable at the point a where the function rule splits 21. Given ( )ts(position function), find ( )tv22. Given ( )tv, find how far a particle travels on ba,23. Find the average velocity of a particle on ba,24. Given ( )tv, determine if a particle is speeding up at t=k25. Given ( )tvand ( )0s, find ( )ts26. Show that Rolle’s Theorem holds on ba,27. Show that Mean Value Theorem holds on ba,28. Find domain of ( )xf29. Find range of ( )xfon ba,30. Find range of ( )xfon ()∞∞-,31. Find ( )xf′by definition 32. Find derivative of inverse to( )xfat ax=
33. yis increasing proportionally to y34. Find the line cx=that divides the area under ( )xfon ba,to two equal areas 35. ( )=∫dttfdxdxa36. ddxf t()au∫dt37. The rate of change of population is … 38. The line bmxy+=is tangent to ( )xfat ()ba,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( )dttfxa∫45. Given a base, cross sections perpendicular to the x-axis are squares 46. Find where the tangent line to ( )xfis horizontal 47. Find where the tangent line to ( )xfis vertical 48. Find the minimum acceleration given ( )tv49. Approximate the value of ()1.0fby using the tangent line to fat 0=x
50. Given the value of ( )afand the fact that the anti- derivative of fis F, find ( )bF51. Find the derivative of ( )()xgf52. Given ( )dxxfba∫, find ( )dxkxfba∫+53. Given a picture of ( )xf′, find where ( )xfis increasing 54. Given ( )tvand ( )0s, find the greatest distance from the origin of a particle on ba,55. Given a water tank with ggallons initially being filled at the rate of ( )tFgallons/min and emptied at the rate of ( )tEgallons/min on 21,tt, find a) the amount of water in the tank at mminutes 56. b) the rate the water amount is changing at m57. c) the time when the water is at a minimum 58. Given a chart of xand ( )xfon selected values between aand b, estimate ( )cf′where cis between a andb.