Values b and c that make the piece wise function differentiable

The video tutorial covers the concepts of continuity and differentiability in mathematics. It begins by explaining the need to find values that make a function continuous and differentiable. The instructor sets up an equation and solves it to ensure continuity at a specific point. The tutorial then checks differentiability by taking derivatives and evaluating them at another point. The process involves solving equations and verifying results, concluding with the final values for the variables involved.

What is the primary condition for a function to be continuous at a point?

• The function must be defined and have a limit at that point.

• The function must be increasing at that point.

• The function must have a limit at that point.

• The function must be differentiable at that point.

What equation is set up to ensure the function is continuous at X = 3?

• 3X^2 + 4X = 2X^3 + BX + 4

• 3X^2 + 4X = 2X^3 + 4X + B

• 3X^2 + 4X = 2X^3 + 4X + C

• 3X^2 + 4X = 2X^3 + BX + C

What is the value of B found during the differentiability check?

• B = 4

• B = 8

• B = 2

• B = 6

How is differentiability checked in the final section?

• By solving for B and C using the original function.

• By taking the derivative of the function and checking its value at X = 1.

• By comparing the left and right limits of the function.

• By ensuring the function is continuous at all points.

What is the final value of C found in the video?

• C = 1

• C = 0

• C = 2

• C = 3