4/30/2015
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10­3 Curve Sk e tching II (6711510)
Due:
Mon Mar 30 2015 09:01 AM MDT
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Read today's Notes and Learning Goals.
Each answer box is limited to 5 submissions.
Warning! After 2 wrong submissions you lose half credit. Don't guess!
In each problem, after you answer (or at least attempt) all of the parts, a
solution will appear. Use it to check your sign chart and your graph.
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Question Details
Concavity w ith chart 1 [3086866]
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You are given f(0) = −5 and f '(x) = x3 − 6x2 + 9x.
1. Find the critical points of the function.
2. Find all points where f ''(x) = 0 or fails to exist.
3. Make a sign chart with three rows.
Row 1 has +/− info for f '. Row 2 has inc/dec info for f '. (Same as +/− for f ''.) Row 3 has the shape of of f in each column.
4. Sketch a graph of f. Then answer the questions below.
Warning! After 2 tries on any answer box you only get half credit. After 5 tries you get none. After one try on each answer box a solution link will appear. Click it to compare your chart and your graph to the solution.
Determine whether each critical point produces a local minimum or maximum (or neither). Enter your answers as a
comma­separated list. If an answer does not exist, enter DNE.
local minimum when x = local maximum when x = Determine the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
increasing decreasing Find the points of inflection of the function. (Enter your answers as a comma­separated list. If an answer does not exist,
enter DNE.)
points of inflection when x = Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
concave up concave down https://www.webassign.net/v4cgijaimos@boisestate/assignments/preview.tpl?aid=6711510&deployment=10659045&UserPass=7b…
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Concavity w ith chart 2 [3086867]
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You are given f(0) = 6 and f '(x) as shown below
Create a full sign chart and a graph of f, as in the previous problem. Then answer the questions below.
Warning! After 2 tries on any answer box you only get half credit. After 5 tries you get none. After one try on each answer box a solution link will appear. Click it to compare your chart and your graph to the solution.
Determine whether each critical point produces a local minimum or maximum (or neither). Enter your answers as a
comma­separated list. If an answer does not exist, enter DNE.
x = local minimum when local maximum when x = Determine the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
increasing decreasing Find the points of inflection of the function. (Enter your answers as a comma­separated list. If an answer does not exist,
enter DNE.)
points of inflection when x = Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
concave up concave down https://www.webassign.net/v4cgijaimos@boisestate/assignments/preview.tpl?aid=6711510&deployment=10659045&UserPass=7b…
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Concavity w ith chart 3 [3086868]
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60
You are given f(x) = . Note that this is f, not the derivative.
12 + x2
1. Find the critical points of the function.
2. Find all points where f ''(x) = 0 or fails to exist.
3. Create the full sign chart, including shape of f.
4. Sketch a graph of f. Then answer the questions below.
Warning! After 2 tries on any answer box you only get half credit. After 5 tries you get none. After you answer all the questions you can check your chart and your graph against the solution.
Determine whether each critical point produces a local minimum or maximum (or neither). Enter your answers as a
comma­separated list. If an answer does not exist, enter DNE.
local minimum when x = local maximum when x = Determine the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
increasing decreasing Find the points of inflection of the function. (Enter your answers as a comma­separated list. If an answer does not exist,
enter DNE.)
points of inflection when x = Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
concave up concave down https://www.webassign.net/v4cgijaimos@boisestate/assignments/preview.tpl?aid=6711510&deployment=10659045&UserPass=7b…
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Question Details
Concavity w ith chart 4 [3086869]
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You are given f(0) = 2 and f '(x) as shown below. Assume that the domain of f is (−2, 4).
Create a full sign chart and a graph of f. Be sure to include endpoints in your chart, but remember that endpoints cannot
be critical points or inflection points. Then answer the questions below.
Warning! After 2 tries on any answer box you only get half credit. After 5 tries you get none. After one try on each answer box a partial solution will appear. Compare your chart to the chart in the solution.
Determine whether each critical point produces a local minimum or maximum (or neither). Enter your answers as a
comma­separated list. If an answer does not exist, enter DNE.
local minimum when x = local maximum when x = Determine the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
increasing decreasing Find the points of inflection of the function. (Enter your answers as a comma­separated list. If an answer does not exist,
enter DNE.)
points of inflection when x = Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation.
Enter EMPTY or ∅ for the empty set.)
concave up concave down Assignment Details
Name (AID): 10­3 Curve Sketching II (6711510)
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Author: Skriletz, Jaimos ( jaimosskriletz@boisestate.edu )
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Last Saved: Dec 19, 2014 08:04 PM MST
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Group: BSU Calculus
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