How to determine if a function is continuous and differentiable

The video tutorial explores the concept of differentiability, emphasizing that a function must be continuous to be differentiable. The instructor highlights a problem where the absence of an equal sign indicates discontinuity, making the function non-differentiable. An attempt to verify differentiability through calculations further confirms the function's non-differentiability.

What is the first step in determining if a function is differentiable?

• Solve the equation

• Find the limit

• Calculate the derivative

• Check if the function is continuous

Why is the absence of an equal sign significant in determining differentiability?

• It shows the function is not continuous

• It indicates the function is linear

• It means the function is quadratic

• It suggests the function is periodic

What conclusion can be drawn if a function is not continuous?

• The function is differentiable

• The function is linear

• The function is not differentiable

• The function is quadratic

In the hypothetical scenario, what was the result of the function values?

• They were not equal

• They were undefined

• They were equal

• They were zero

What does the hypothetical scenario demonstrate about the function?

• The function is linear

• The function is continuous

• The function is differentiable

• The function is not differentiable