How to show that a solution exists to a functions using IVT

The video tutorial explains how to apply the Intermediate Value Theorem (IVT) to a continuous function defined on a closed interval. The function is evaluated at the endpoints to demonstrate that it takes on both negative and positive values, indicating that there must be a point where the function equals zero. The tutorial emphasizes the importance of continuity and closed intervals in applying the IVT and concludes by confirming the existence of a solution without specifying its exact location.

What is the main purpose of applying the Intermediate Value Theorem (IVT) in this context?

• To prove that a value exists where the function crosses the X-axis

• To find the exact value where the function crosses the X-axis

• To determine the maximum value of the function

• To calculate the derivative of the function

What is the value of the function at the endpoint zero?

• 0

• 2

• -2

• 28

What does the function value at two indicate about the function's behavior?

• The function is positive

• The function is negative

• The function is constant

• The function is decreasing

Why is it important that the function is continuous on the interval?

• It guarantees the function is differentiable

• It means the function is increasing

• It ensures the function has a maximum value

• It allows the use of the Intermediate Value Theorem

What conclusion can be drawn from the application of the IVT in this scenario?

• The function has no roots

• The function is not continuous

• There is a root between zero and two

• The function is always positive