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Let f(x) = x³ − 4x² + 2x − 8. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x = Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of a values or the word "none".

Let f(x) = x³ − 4x² + 2x − 8. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x = Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of a values or the word "none".

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Let f(x) = x³ 4x² + 2x - 8. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at a = 1. Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of a values or the word "none".
Transcribed Image Text:Let f(x) = x³ 4x² + 2x - 8. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at a = 1. Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of a values or the word "none".
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f(x)=x3-4x2+2x-8for inflection points f''(x)=0d dx(xn)=nxn-1if f''(x)>0, than concave upif f''(x)<0, than concave down 

 

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