Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3 ✓
3x² − 3 = 0
∴ x = −1, 1 ✓
f″(x) = 6x
f″(−1) = −6 < 0 ✓
f″(1) = ?
Show why this is a minimum
GradeOS · Sample material3 / 4
AssignmentsDemo data
Every page in its place.
Mathematics · Turning points
Student A011 answer pageIn review
Student A021 answer pageOrganized
Student A031 answer pageOrganized
Student A041 answer pageOrganized
Student A051 answer pageOrganized
12 assignments · 12 students
Class analysisDemo data
See the shared question.
Question 04 · 12 students
7 / 12need a complete classification
00
01
32
43
54
Score below · Student count above
Find the focus for your next lesson
AssistantDemo data
What is worth teaching again?
GradeOS
Revisit how to classify a turning point.
In these sample assignments, 7 of 12 students have not fully justified their classifications. Start by distinguishing finding a stationary point from classifying it, then refer back to their work.
A01 · Question 04
Answers connected to their sources
Teacher reviewDemo data
The final decision is yours.
3 / 4
Review the original work and the rubric. Keep the final judgment with the teacher.
A01 · Question 04Demo data
RubricDemo data
A reason for every mark.
Question 04 · f(x) = x³ − 3x
01Correct derivative1 / 1
02Both stationary points1 / 1
03Classify the maximum1 / 1
04Classify the minimum0 / 1
A stationary point alone does not establish an extremum. Use a sign change or the second derivative.
Linked to the original answer3 / 4
Mathematics · Student workDemo data
Derivatives & turning points04
Student A014 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3
3x² − 3 = 0
∴ x = −1, 1
f″(x) = 6x
f″(−1) = −6 < 0
f″(1) = ?
Original student work
GradeOS · Sample material01 / 01
GradeOS
Less grading.
More teaching.
Students do the thinking.
You see what matters.
GradeOS
Less grading.
More teaching.
Students do the thinking.
You see what matters.
GradeOS
Every score.
A clear reason.
Students do the thinking.
You see what matters.
GradeOS
Real students.
Real progress.
Students do the thinking.
You see what matters.
GradeOSStudents do the thinking.
You see what matters.
04 / D
A stationary point. What next?
x = 1 is stationary. To classify it as a minimum, show that f″(1) > 0, or that the first derivative changes from negative to positive.
RubricDemo data
A reason for every mark.
Question 04 · f(x) = x³ − 3x
01Correct derivative1 / 1
02Both stationary points1 / 1
03Classify the maximum1 / 1
04Classify the minimum0 / 1
A stationary point alone does not establish an extremum. Use a sign change or the second derivative.
Linked to the original answer3 / 4
Teacher reviewDemo data
Your judgment, confirmed.
3 / 4
Review the original work and the rubric. Keep the final judgment with the teacher.
A01 · Question 04Demo data
Mathematics · Student workDemo data
Derivatives & turning points04
Student A024 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3 ✓
3x² − 3 = 0
∴ x = −1, 1 ✓
f″(x) = 6x
f″(−1) = −6 < 0 ✓
f″(1) = 6 > 0
Classification supported
GradeOS · Sample material4 / 4
Mathematics · Student workDemo data
Derivatives & turning points04
Student A034 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3 ✓
3x² − 3 = 0
∴ x = −1, 1 ✓
f″(x) = 6x
f″(−1) = −6 < 0 ✓
f″(1) = ?
Show why this is a minimum
GradeOS · Sample material3 / 4
Mathematics · Student workDemo data
Derivatives & turning points04
Student A044 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3 ✓
3x² − 3 = 0
∴ x = −1, 1 ✓
f″(x) = 6x
f″(−1) = −6 < 0 ✓
f″(1) = 6 > 0
Classification supported
GradeOS · Sample material4 / 4
Mathematics · Student workDemo data
Derivatives & turning points04
Student A054 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
f′(x) = 3x² − 3 ✓
3x² − 3 = 0
∴ x = −1, 1 ✓
f″(x) = 6x
f″(−1) = −6 < 0 ✓
f″(1) = ?
Show why this is a minimum
GradeOS · Sample material3 / 4
Mathematics · Student workDemo data
Derivatives & turning points04
Student A064 marks
f(x) = x³ − 3x
Find the stationary points and classify each as a local maximum or minimum.
Trust comes from control points visible in the product: original material, teacher review, separate publication, and public privacy and support guidance.
01
Original material stays beside the result
Answer sheets, page order, and student boundaries can be checked before grading and revisited during review.
02
Review and publish remain separate actions
Teachers inspect high-impact results, evidence, and rubric points first; only then do they decide what to publish.
03
Privacy, support, and deletion paths stay public
Account and data guidance is not hidden inside sales copy. Teachers can read it directly or make a request.
