What is the primary focus of differentiability at a point?

Understanding Differentiability and Continuity

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Mathematics
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11th Grade - University
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Hard

Aiden Montgomery
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
To calculate the area under the curve at a point
To find the slope of the tangent line at a point
To check if a function is increasing or decreasing at a point
To determine if a function is continuous at a point
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if a function is differentiable at a point?
The function is not defined at that point
The function is decreasing at that point
The function is continuous at that point
The function has a maximum at that point
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If a function is not continuous at a point, what can be said about its differentiability?
It might be differentiable
It is definitely differentiable
It is undefined
It is not differentiable
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the slope of a function with a discontinuity as x approaches the point of discontinuity?
The slope approaches infinity
The slope approaches zero
The slope becomes undefined
The slope remains constant
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a removable discontinuity?
A point where the function can be redefined to be continuous
A point where the function has a jump
A point where the function has a vertical asymptote
A point where the function is not defined
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does a removable discontinuity affect differentiability?
It makes the function continuous
It has no effect on differentiability
It prevents the function from being differentiable
It makes the function differentiable
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Can a function be continuous at a point but not differentiable? Provide an example.
Yes, for example, a linear function
Yes, for example, the absolute value function
No, all continuous functions are differentiable
No, it cannot
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