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
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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Transcribed Image Text:Tutorial Exercise
The graph of the second derivative f" of a function f is shown. State the x-coordinates of the inflection points of f.
Part 1 of 5
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:
(smallest value)
Part 2 of 5
Part 3 of 5
X =
Part 4 of 5
X =
Sony
5 6 7 8 9 10
X
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.
Submit
✓
After x = 3, f"(x) is above ✔
an inflection point.
9 (largest value)
X =
Using this logic, we see that f"(x) does not ✔
above the x-axis, indicating that f"(x) is positive
Part 5 of 5
Finally, at x = 9, we see f "(x) changes sign from [positive
is
v ✓ an inflection point.
So, the x-coordinates of the inflections points are:
(smaller value)
(larger value)
Skip (you cannot come back)
does not change sign at x = 5, and so x = 5
positive. This means that f(x) changes concavity from concave down
✓ before x = 9 to negative
✓
is not
is not an inflection point.
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
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