Calculus Index Cards

1. Calculus Index Cards Front And Back

2. Instructions • The odd numbered slides are the front of the index card, the questions • The even numbered slides are the back, the answers • Write the front of the card and then write the back and carry the stack with you at all times

3. Given Velocity and Position at t = 0 Front • Find speed • Acceleration • Position Function • Distance traveled

4. Back

5. Front • Given position find average velocity from a to b • Given a table of amounts, find the rate of change at one of those amounts • Given a function from a, to b, find the average value • Given velocity from a to b, find the average velocity

6. Given position find average velocity from a to b old fashion slope from a to b • Given a table of amounts, find the rate of change at one of those amounts Old fashion slope around that point • Given a function from a, to b, find the average value • Given velocity from a to b, find the average velocity

7. Given A. Use the left hand rule B. Use the right hand rule C. Use the midpoint rule D. Use the trapezoid rule

8. Given A. Use the left hand rule B. Use the right hand rule C. Use the midpoint rule D. Use the trapezoid rule

9. Find the equation of the line tangent to the curve • Find the equation of the line normal

11. Given And the graph of f(x) • Find g(some number) • Find g’(x), find g’(some number) • Find where g has a max/min • Find the point of inflection of g

12. Given And the graph of f(x) • Find g(some number) • Find g’(x), find g’(some number) • Find where g has a max/min • Find the point of inflection of g

13. Function is continuous if (informal definition) (Formal definition) Function is differentiable if (informal) (formal)

14. Function is continuous if (informal definition) (Formal definition) Function is differentiable if (informal) (formal)

15. Mean Value theorem Extreme Value Theorem

19. The derivative of this Is this

20. The derivative of this Is this

21. The derivative of is

22. The derivative of is

23. The derivative of is

24. The derivative of is

25. The first derivative tells us about

26. The first derivative tells us about • Slope Instantaneous rate of change Increasing or decreasing • Max, min

27. The second derivative tells us

28. The second derivative tells us • Concave up concave down • Point of inflection • Rate of change of the slopes • The maximum/minimum slope

29. Product rule Quotient rule Chain rule

30. Product rule Quotient rule Chain rule

31. The antiderivative of is

32. The antiderivative of is

33. The antiderivative of is

34. The antiderivative of is

35. What is this? or

36. What is this? or Definition of the derivative

37. Find the answer

38. Find the answer

39. First derivative test • f’<0 when x<a and f’>0 when x>a. What does that mean at x = a • f’>0 when x<a and f’<0 when x>a. What does that mean at x = a

40. First derivative test • f’<0 when x<a and f’>0 when x>a. What does that mean for x = a • a is a min • f’>0 when x<a and f’<0 when x>a. What does that mean for x = a • a is a max

41. Second derivative Test • f ’(a) = 0 and f ”(a)<0. What does that mean at f(a)? • f ’(a) = 0 and f ”(a)>0. What does that mean at f(a)?

42. Second derivative Test • f ’(a) = 0 and f ”(a)<0. What does that mean at f(a)? • f(a) is a max • f ’(a) = 0 and f ”(a)>0. What does that mean at f(a)? • f(a) is a min

43. What is the general solution for the following

44. What is the general solution for the following

45. Find the derivative of the following

46. Find the derivative of the following

47. underestimate or overestimate? • left hand rule with a function that is increasing • right hand rule with a function that is increasing • tangent line approximation with a curve that is concave down • tangent line approximation with a curve that is concave up

48. underestimate or overestimate? • left hand rule with a function that is increasing - under • right hand rule with a function that is increasing - over • tangent line approximation with a curve that is concave down - over • tangent line approximation with a curve that is concave up - under

49. is speed increasing or decreasing • velocity is positive and acceleration is negative • velocity is negative and acceleration is negative

50. is speed increasing or decreasing • velocity is positive and acceleration is negative - decreasing • velocity is negative and acceleration is negative - increasing