The graph of the second derivative f" of a function fis shown. State the x-coordinates of the inflection points of f. Part 1 of 5 JA We know that possible inflection points of f(x) occur where F"(x) = 0. These will be the points where the graph of f "(x) crosses the x-axis. The x-values of these points are: 3 (smallest value) 5 9 (largest value) Part 2 of 5 We know that f"(x) = 0 at x = 3, x = 5, and x= 9. However, this alone is not enough to indicate an inflection point. There must be a concavity change in f(x), which is indicated by a sign change in F"(x). For example, at x=3 we see that f"(x) is below✔ below the x-axis before x = 3, which means that f(x) is negative ✔ negative Part 3 of 5 After x = 3, f"(x) is above ✔✔ an inflection point. Part 4 of 5 x= 10 Using this logic, we see that "(x) does not ✓ Part 5 of 5 Finally, at x = 9, we see f"(x) changes sign from positive ✔✔✔an inflection point. is So, the x-coordinates of the inflections points are: above the x-axis, indicating that f"(x) is positive (smaller value) (larger value) Submit Skip.(you cannot come back) positive. This means that f(x) changes concavity from concave down✔ does not change sign at x = 5, and so x = 5 is not✔ is not an inflection point. before x = 9 to negative ✔✔✔afterward. Therefore, f(x) changes concavity from concave up down before x = 3 to concave up✔ before x = 9 to concave down up afterward, and so x= 3 is ✔✔✔afterward, and so x=9
The graph of the second derivative f" of a function fis shown. State the x-coordinates of the inflection points of f. Part 1 of 5 JA We know that possible inflection points of f(x) occur where F"(x) = 0. These will be the points where the graph of f "(x) crosses the x-axis. The x-values of these points are: 3 (smallest value) 5 9 (largest value) Part 2 of 5 We know that f"(x) = 0 at x = 3, x = 5, and x= 9. However, this alone is not enough to indicate an inflection point. There must be a concavity change in f(x), which is indicated by a sign change in F"(x). For example, at x=3 we see that f"(x) is below✔ below the x-axis before x = 3, which means that f(x) is negative ✔ negative Part 3 of 5 After x = 3, f"(x) is above ✔✔ an inflection point. Part 4 of 5 x= 10 Using this logic, we see that "(x) does not ✓ Part 5 of 5 Finally, at x = 9, we see f"(x) changes sign from positive ✔✔✔an inflection point. is So, the x-coordinates of the inflections points are: above the x-axis, indicating that f"(x) is positive (smaller value) (larger value) Submit Skip.(you cannot come back) positive. This means that f(x) changes concavity from concave down✔ does not change sign at x = 5, and so x = 5 is not✔ is not an inflection point. before x = 9 to negative ✔✔✔afterward. Therefore, f(x) changes concavity from concave up down before x = 3 to concave up✔ before x = 9 to concave down up afterward, and so x= 3 is ✔✔✔afterward, and so x=9
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 2WE
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