How to determine the points that make the function differentiable

The video tutorial explains how to make a function differentiable by ensuring it is continuous. It discusses the importance of limits from the left and right being equal and checks the derivatives to ensure differentiability. The process involves setting up equations to solve for variables a and b, ensuring the function is both continuous and differentiable. The tutorial concludes with solving these equations to find the values of a and b.

What is the first condition that must be satisfied for a function to be differentiable?

• The function must be decreasing.

• The function must be continuous.

• The function must have a maximum point.

• The function must be increasing.

When checking for differentiability, what must be true about the derivatives from the left and right?

• They must be negative.

• They must be equal.

• They must be zero.

• They must be positive.

In the context of this lesson, what does it mean if a function has a hole?

• The function is not continuous.

• The function is differentiable.

• The function is linear.

• The function has a maximum point.

What is the value of 'a' that makes the function differentiable?

• 1

• 1/4

• 1/3

• 1/2

What is the value of 'b' that ensures the function is differentiable?

• -4/3

• -2/3

• -3/4

• -1/3