# Math-Part 2

The flashcards below were created by user clkottke on FreezingBlue Flashcards.

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)
 Author: clkottke ID: 302386 Card Set: Math-Part 2 Updated: 2015-05-08 22:20:51 Tags: pre algebra calculus statistics linear Folders: Description: Review Show Answers:
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}