Differentiability with Graph Day 1 2024 UPDATED)

Differentiability with Graph Day 1 2024 UPDATED)

Assessment

Flashcard

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

Front

What is differentiability in calculus?

Back

Differentiability refers to the existence of a derivative of a function at a given point. A function is differentiable at a point if it has a defined tangent line at that point.

2.

FLASHCARD QUESTION

Front

What does it mean for a function to be continuous?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

3.

FLASHCARD QUESTION

Front

Can a function be continuous but not differentiable? Give an example.

Back

4.

FLASHCARD QUESTION

Front

What is a sharp turn in a graph?

Back

A sharp turn in a graph occurs when the direction of the graph changes abruptly, making it impossible to draw a single tangent line at that point.

5.

FLASHCARD QUESTION

Front

What is the relationship between continuity and differentiability?

Back

For a function to be differentiable at a point, it must be continuous at that point. However, continuity alone does not guarantee differentiability.

6.

FLASHCARD QUESTION

Front

What is the significance of the slope of the tangent line?

Back

The slope of the tangent line at a point on a function represents the derivative of the function at that point, indicating the rate of change of the function.

7.

FLASHCARD QUESTION

Front

In which quadrant can a function be non-differentiable?

Back

A function can be non-differentiable in any quadrant, typically where there are sharp turns or discontinuities.

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