# FTCE Math Review Deck 2

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1. What are 5 conditions in which f(x) does not have a derivative at x = c?
• 1.  f(x) is discontinuous at x=c.
• 2.  f(x) has a vertical tangent at x=c.
• 3.  f(x) has a cusp at x=c.
• 4.  f(x) has a corner at x=c.
• 5.  f(x) has a vertical asymptote at x=c.
2. For a rational function , if the degree of p(x) > degree of q(x), then
0
3. For a rational function , if the degree of p(x) = degree of q(x), then
k, where k=ratio of the p and q's leading coefficients
4. For a rational function , if the degree of p(x) < degree of q(x), then
, which is also interpreted that the limit does not exist
5. The average rate of change over an interval is equal to __________.
the slope of the secant line
6. The instantaneous rate of change at any point is equal to _____________.
the slope of the line tangent to the point.
7.
8. What is a critical point on a graph?
a place where the derivative is 0 or is undefined
9. Any point on the graph at which the first derivative is zero represents a ____________.
minimum or maximum
10. To determine if a critical point is a maximum or minimum you should __________.
evaluate two points  and  and compare the change in slope
11. The first derivative measures ________.
The second derivative measures __________.
• the slope of the function
• the change in the slope of the function (concavity)
12. If , g(x) is concave ______.
upward
13. If , then g(x) is said to be concave ________.
downward
14. The points of inflection are where the first derivative _____________.
changes sign (negative to positive or positive to negative)
15. Using the 2nd Derivative Test:
f(x)        f'(x)       f''(x)
?            =0         >0
?            =0         <0
?            =0         =0
• min
• max
• no determination can be made
16. Fundamental theorem of calculus:
F(b) - F(a)
17. For a portion of a function lying below the x-axis in range [c,d], find the area by calculating:
18. To find the area between 2 curves:
Area = ?
• where:
• f(x) is the top/right curve
• g(x) is the bottom/left curve
19. The symbol  means _________.
• Union
•  B = in A, in B, or in both
20. The symbol  means _______.
• intersection
•  B = elements A and B have in common
21. The symbol  means _______.
subset
22. The symbol  means _______.
is an element of
 Author: akrell ID: 232594 Card Set: FTCE Math Review Deck 2 Updated: 2013-09-03 18:24:32 Tags: calculus trig math Folders: Description: Second set of review cards for the Florida Teacher Certification Exam in Mathematics (grades 6-12) Show Answers: