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Math-Part 2

  1. The Power Rule:
    if 
    Image Upload 2
    then f'(x) =
    Image Upload 4
  2. If f(x) = sin x then f'(x) = ?
    f'(x) = cos x
  3. if f(x) = cos x then f'(x) =
    f'(x) = -sin x
  4. If f(x) = tan x then f'(x) =
    Image Upload 6
  5. If f(x) = cot x then f'(x) =
    Image Upload 8
  6. If f(x) = sec x then f'(x) =
    f'(x) = sec x tan x
  7. If f(x) = csc x then f'(x) =
    f'(x) = -csc x cot x
  8. Chain Rule (composite functions)
    If
     Image Upload 10
    then
    f'(x) =
    f'(x)= g'[f(x)]f'(x)
  9. If
     Image Upload 12
    what is the domain?
    what is f'(x)?
    • Domain: Image Upload 14
    • Image Upload 16
  10. If 
    Image Upload 18
    What is the domain?
    What is f'(x)?
    Domain:  Image Upload 20

    Image Upload 22
  11. If 
    Image Upload 24

    What is the domain?
    What is f'(x)?
    Domain:  Image Upload 26
  12. If 
    Image Upload 28
    What is the domain?
    What is f'(x)?
    • Domain: Image Upload 30
    • Image Upload 32
  13. If
    Image Upload 34
    What is the domain?
    at is f'(x)?
    • Domain:  Image Upload 36
    • Image Upload 38

    Image Upload 40
  14. If
    Image Upload 42
    What is the domain?
    What is f'(x)?
    • Domain:  Image Upload 44
    • Image Upload 46

    Image Upload 48
  15. If
    Image Upload 50
    What is f'(x)?
    Image Upload 52
  16. If 
    Image Upload 54; a > 0; a Image Upload 56 1
    What is f(x)?
    Image Upload 58
  17. If
    Image Upload 60
    What is f'(x)?
    Image Upload 62
  18. If 
    Image Upload 64
    a > 0 
    aImage Upload 661
    What is f'(x)
    Image Upload 68
  19. What are four things derivatives are used for?
    • 1. curve, and sketching.
    • 2. solving maximum and minimum problems.
    • 3. related rate problems.
    • 4. approximating function values.
  20. What are the (3) steps to finding the equation of the tangent line at a point?
    • 1. Take the derivative of f(x).
    • 2. Find f'(x)=y
    • 3. Using y-y1=-m(x-x1) to find the equation.
  21. Where are the critical points?
    • 1. where f'(x) = 0
    • 2. where f'(x) = does not exist.
  22. The ______ ______ theorem states that if f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and minimum value on [a,b]
    Extreme Value Theorem
  23. The relationship between the slope of a tangent line to a curve and the secant line through points on a curve at the end points of an interval is the ______ ______ Theorem.
    Mean Value
  24. What is f'(c) defined as in the Mean Value Theorem?
    Image Upload 70
  25. Distance =
    (rate)(time)
Author
clkottke
ID
302386
Card Set
Math-Part 2
Description
Review
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