second derivative test...
TRANSCRIPT
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:07 PM
AP Calculus: Concavity
a) Determine where f(x)=x3+6x215x+13 is increasing and decreasing?
b) What are the relative maximum and minimum of f(x)?
p. 298299 # 11, 32ad, 33ac
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second derivative test concavity.notebook
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November 13, 2013
Nov 1211:44 AM
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:11 PM
Concavity:
f(x) is concave down on an interval I if all of the tangents to the curve on I are above the graph of f(x)
f(x) is concave up on an interval I if all of the tangents to the curve on I are below the graph of f(x)
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:16 PM
A function f(x) can be concave up, and either increasing or decreasing.
A function f(x) can be concave down, and either increasing or decreasing.
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:22 PM
Where is the following function concave up? concave down?
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:27 PM
A point P on a curve y=f(x) is called an inflection point if f is continuous there and the curve changes from concave upward to concave downward or form concave downward to concave upward at P.
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:26 PM
2nd Derivative test for Concavity:
If f ''(x)>0 for all x in some interval I then the graph of f is concave upward on I.
If f ''(x)
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:39 PM
Using the graph of f'(x) below, find the points of inflection of f and determine where the function f is concave upward and where it is concave downward.
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:31 PM
Find the points of inflection of f(x)=x3+6x215x+13 and determine the intervals where the function f is concave upward and where its is concave downward.
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:32 PM
Find the points of inflection of f(x)=4x44x2 and determine the intervals where the function f is concave upward and where it is concave downward.
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second derivative test concavity.notebook
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November 13, 2013
Nov 107:39 PM
The graph of f is shown below and f is twice differentiable. Which of the following statements is true:
1.f(1)
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second derivative test concavity.notebook
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November 13, 2013
Nov 1210:51 PM
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