Calculus

Calculus

1. 1. A derivative is a value derived from an underlying asset.

2. 2. A mathematical derivative is an instantaneous rate of function in regards to one variable.

3. 3. Using algebra to find the slope of a curve.

4. 4. 2x

5. 5. 0

6. 6. cos(x)

7. 7. -sin(x)

8. 8. e^(x)

9. 9. 1

10. 10. 1/x

11. 11. 0

12. 12. 0

13. 13. 2fg

14. 14. 2f/g

15. 15. y

16. 16. a straight line which touches a curve in one point

17. 17. the line that goes through the point and is perpendicular to the tangent line.

18. 18. 1

19. 19. 1

20. 20. 2

21. 21. 2a

22. 22. max: x=a/ Min:x=b

23. 23. false, because the curve can max out or go both ways.

24. 24. False, they must have at least one point of inflection.

25. 25. Highest and lowest points of a function.

26. 26. (f composed g)^1 = (f composed g) * g^1

27. 27. When differentiating a function of a function

28. 28. 0

29. 29. 0

30. 30. 1/x

31. 31. -1/x^2

32. 32. 0

33. 36. Using the graph menu on the calculator

34. 37. Using G-solve menu

35. 38. Using the graph menu, on the sketch menu

36. 39. Using the integers function

37. 40. if its negative at the left min, positive at the left Max,

38. 41. f^1(x)=0 and second derivative is positive then min. f^1(x)=0 second derivative is negative then max.

39. 42. concave up corresponds to a positive second derivative, concave down corresponds to negative second derivative, when the function changes from concave up to concave down or vice versa the second derivative must equal zero.

40. 43. prime candidates when function is real.

41. 44. are x values where the second derivative is equal to zero or not defined.

42. 45. they are the same

43. 46. using 100 fences, how to have the biggest area fenced.

44. 47. 1250

45. 48. an anti definitive integral with no start or end values.

46. 49. an integral with start and end values.

47. 50. one of the antiderivatives of some function may be obtained as the integral with a variable bound of integration.

48. 51. eliminating all x values.

49. 52. pressing F4, then F6 then F1 and substituting values

50. 53. using the graph menu.