Differentiability with Graph Day 1 2024 UPDATED)

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.

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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.

Front

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

Back

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.

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.

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.

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.

Front

What does it mean if a function is not differentiable at a point?

Back

If a function is not differentiable at a point, it means that the derivative does not exist at that point, often due to a sharp turn or discontinuity.

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

What is an example of a function that is not differentiable everywhere?

Back