Learn how to determine if a function is continuous and differentiable piecewise

The video tutorial explains the importance of checking continuity before differentiability in mathematical functions. It uses an example at X=1 to demonstrate how a function can have equal derivatives on both sides but still not be continuous, thus not differentiable. The tutorial emphasizes that continuity is a prerequisite for differentiability.

What is the first step to check when analyzing a function for differentiability?

• Check if the function is continuous

• Check if the function is differentiable

• Check if the function is integrable

• Check if the function is linear

In the example given, what was the conclusion about the function's continuity at X = 1?

• The function is continuous

• The function is not continuous

• The function is linear

• The function is differentiable

Why is it important to check continuity before differentiability?

• Because continuity ensures integrability

• Because differentiability ensures linearity

• Because a function can be differentiable but not continuous

• Because a function can be continuous but not differentiable

What happens if you only check differentiability without checking continuity?

• You might incorrectly conclude the function is differentiable

• You might incorrectly conclude the function is integrable

• You might incorrectly conclude the function is linear

• You might incorrectly conclude the function is continuous

What is the result of having the same derivatives on both sides of a point if the function is not continuous?

• The function is differentiable

• The function is not differentiable

• The function is linear

• The function is integrable