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Utah
Brigham Young University
Calculus
Calculus 112
Wadley
test 3
test 3
Calculus 112
with
Wadley
at
Brigham Young University
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Chandler F.
Created:
20140311
Last Modified:
20140312
Size:
19
Views:
2
when using the I/D test what is important?
to know where
: f'(x) >0
:f'(x)<0
use critical numbers to create intervals

if f' changes from positive to negative at c, then...
then f has a local maximum at c
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if f' changes from negative to positive at c, then...
then f has a local minimum at at c
if f' does not change sign at c, then...
then f has no local max or min at c
if a graph lies above it's tangent lines, then it is called_____
upward concave
if a graph lies below its tangent lines, then it is called _______
downward concave
if f"(x) > 0 for the x values in I, then the graph is concave ____.
upward
if f"(x)<0 for all x in I, then the graph is concave _______.
downward
what is the inflection point of the curve?
when it changes from upward to downward concave or vice versa
there is a point of inflection anywhere that the second derivative...
changes sign
if f'(c)=0 &
f"(c)>0
then ______
then f has a local minimum at c
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if f'(c)=0 &
f"(c)<0
then what?
then f has a local maximum at c
how do I use the Second Derivative Test?
1. take f'(x
)
2. take f"(x)
3. set f'(x)=0
4. plug critical #s into f"(x)
if f"(c)=0 then ...
then the test is inconclusive
if f"(c) doesn't exist then...
then the test is inconclusive
inflection points on f(x) will...
change between downward and upward concave
inflection points of f'(x) will...
change between negative and positive slope
inflection points on f"(x) will...
cross the axis
what are the indeterminate powers?
0
^{inf}
, inf
^{0 }
, 1
^{inf}
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