Check continuity and differentiability of a piecewise function

The video tutorial explains how to ensure a function is continuous and its derivatives are equal at a specific point, X = 3. It involves setting up an equation, checking continuity, ensuring derivative equality, and verifying the solution by plugging in values.

What condition must be met for a function to be continuous at X = 3?

• The derivative must be zero.

• The function must be undefined.

• X squared must equal six times X minus nine.

• X squared must equal a constant.

Why is it important for the derivatives to be equal at X = 3?

• To make the function continuous.

• To ensure the function is differentiable at that point.

• To solve for X.

• To find the maximum value of the function.

What equation is used to ensure the derivatives are equal at X = 3?

• Derivative equals zero.

• X equals three.

• 2X equals six.

• X squared equals six.

What is the value of X that satisfies the derivative condition?

• X = 2

• X = 5

• X = 4

• X = 3

What is the final step to verify the solution?

• Plug in the value of X and confirm the equality.

• Differentiate the function again.

• Solve for another variable.

• Check if X equals zero.