How is a turning point defined in terms of gradient?

Graph Analysis: Points of Inflection

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard

Mia Campbell
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Where the gradient is zero.
Where the gradient is undefined.
Where the gradient changes from positive to negative or vice versa.
Where the gradient is always positive.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main difference between stationary points and turning points?
Stationary points always have a zero gradient.
All turning points are stationary points.
All stationary points are turning points.
Turning points always have a zero gradient.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Can a turning point exist without being a stationary point?
Yes, if the gradient is zero.
No, it must always have a zero gradient.
Yes, if the gradient changes sign but is not differentiable.
No, it must always be a stationary point.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What marks a point of inflection on a graph?
A point where the gradient is zero.
A change in the sign of the concavity.
A change in the sign of the gradient.
A point where the graph is not continuous.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which method is NOT a way to find a point of inflection?
Looking for discontinuities in the graph.
Finding where the second derivative is zero.
Finding where the first derivative is zero.
Checking for changes in concavity.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a practical way to identify points of inflection on a graph?
Calculating the first derivative.
Using a table of values.
Looking for points where the graph is horizontal.
Covering parts of the graph to see changes in concavity.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if water rests in a part of the graph?
The graph has a turning point.
The graph is concave down.
The graph is concave up.
The graph has a stationary point.
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