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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.

For a rational function , if the degree of p(x) > degree of q(x), then
0

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

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

The average rate of change over an interval is equal to __________.
the slope of the secant line

The instantaneous rate of change at any point is equal to _____________.
the slope of the line tangent to the point.




What is a critical point on a graph?
a place where the derivative is 0 or is undefined

Any point on the graph at which the first derivative is zero represents a ____________.
minimum or maximum

To determine if a critical point is a maximum or minimum you should __________.
evaluate two points and and compare the change in slope

The first derivative measures ________.
The second derivative measures __________.
 the slope of the function
 the change in the slope of the function (concavity)

If , g(x) is concave ______.
upward

If , then g(x) is said to be concave ________.
downward

The points of inflection are where the first derivative _____________.
changes sign (negative to positive or positive to negative)

Using the 2nd Derivative Test:
f(x) f'(x) f''(x)
? =0 >0
? =0 <0
? =0 =0
 min
 max
 no determination can be made








Fundamental theorem of calculus:
F(b)  F(a)

For a portion of a function lying below the xaxis in range [c,d], find the area by calculating:

To find the area between 2 curves:
Area = ?
 where:
 f(x) is the top/right curve
 g(x) is the bottom/left curve

The symbol means _________.
 Union
 A B = in A, in B, or in both

The symbol means _______.
 intersection
 A B = elements A and B have in common

The symbol means _______.
subset

The symbol means _______.
is an element of

