Math-Part 2

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Author:
clkottke
ID:
302386
Filename:
Math-Part 2
Updated:
2015-05-08 18:20:51
Tags:
pre algebra calculus statistics linear
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Review
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  1. The Power Rule:
    if 

    then f'(x) =
  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) =
  5. If f(x) = cot x then f'(x) =
  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
     
    then
    f'(x) =
    f'(x)= g'[f(x)]f'(x)
  9. If
     
    what is the domain?
    what is f'(x)?
    • Domain: 
  10. If 

    What is the domain?
    What is f'(x)?
    Domain:  

  11. If 


    What is the domain?
    What is f'(x)?
    Domain:  
  12. If 

    What is the domain?
    What is f'(x)?
    • Domain: 
  13. If

    What is the domain?
    at is f'(x)?
    • Domain:  

  14. If

    What is the domain?
    What is f'(x)?
    • Domain:  

  15. If

    What is f'(x)?
  16. If 
    ; a > 0; a  1
    What is f(x)?
  17. If

    What is f'(x)?
  18. If 

    a > 0 
    a1
    What is f'(x)
  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?
  25. Distance =
    (rate)(time)

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