How to points on a graph where the function is not differentiable

The video tutorial explains the concept of non-differentiability in functions. It highlights that functions are not differentiable at points where they are not continuous, have vertical tangents, or have corners. Examples include the cube root function, which has a vertical tangent, and specific points like X = 0, 2, and 4 where the function G of X is not differentiable.

What is a basic condition for a function to be non-differentiable?

• It must have a horizontal tangent.

• It must be non-continuous.

• It must be continuous.

• It must be linear.

Why is the cube root function not differentiable at certain points?

• It is linear.

• It has a vertical tangent.

• It is continuous.

• It has a horizontal tangent.

What happens to the derivative of a function at a vertical tangent?

• It becomes negative.

• It remains constant.

• It becomes infinite.

• It becomes zero.

What characteristic of a corner makes a function non-differentiable?

• Abrupt change in direction.

• Continuous curve.

• Smooth transition.

• Constant slope.

At which points is the function G(x) not differentiable?

• X = 1, 3, 5

• X = 0, 2, 4

• X = 2, 4, 6

• X = 1, 2, 3