# 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 Folders: Description: Review Show Answers:

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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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