How to determine the points of differentiability

The video tutorial explains how to determine the values of A and B for which a function is differentiable. It begins by discussing the importance of continuity and differentiability, emphasizing that a function must be continuous to be differentiable. The tutorial then demonstrates how to check for continuity by equating the limits from the left and right. It proceeds to form equations based on these limits and checks the derivatives from both sides to ensure they are equal. Finally, the tutorial solves the equations to find the specific values of A and B that make the function differentiable.

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

• Calculate the derivative from the right-hand side.

• Find the second derivative.

• Check if the function is continuous from the left-hand side.

• Determine if the function is increasing.

What equation is derived to ensure the function is continuous at a point?

• A - B = 2

• A + B = 2

• A * B = 2

• A / B = 2

Why is it important to check the left and right-hand derivatives?

• To determine the function's range.

• To find the maximum value of the function.

• To verify the function is differentiable.

• To ensure the function is continuous.

What is the value of A that makes the function differentiable?

• -3

• 3

• 5

• -5

What is the value of B that makes the function differentiable?

• -5

• 5

• 3

• -3