Find the values a and b that make the function differentiable

The video tutorial covers the concept of differentiability, explaining the conditions required for a function to be differentiable, such as continuity and equal derivatives on both sides of a point. It demonstrates how to check continuity and differentiability at a specific point, using a piecewise function as an example. The tutorial also includes solving systems of equations to find values that make the function differentiable, and discusses different solving methods and error checking.

What are the two conditions that must be met for a function to be differentiable?

• The function must be continuous and have a maximum point.

• The function must have equal derivatives on both sides and be increasing.

• The function must be continuous and have a constant slope.

• The function must be continuous and have equal derivatives on both sides.

At which point is continuity checked in the example provided?

• At x = 2

• At x = 0

• At x = 1

• At x = 5

What is the derivative of the function 3 - x?

• -1

• 1

• 0

• 3

What is the second equation derived from checking differentiability?

• 1 = 2A + B

• -1 = -2A + B

• 0 = A + B

• -1 = A - B

What method is used to solve the system of equations in the example?

• Matrix method

• Substitution method

• Graphical method

• Elimination method

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

• -5

• 5

• -3

• 3

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

• 3

• -3

• -5

• 5