Apply the evt and find extrema on a closed interval

The video tutorial explains the application of the Extreme Value Theorem (EVT) to find extrema of a function on a closed interval. It covers the conditions for EVT, finding critical values using derivatives, and evaluating endpoints. The tutorial emphasizes the importance of clarity in presenting solutions and checking work to avoid errors.

What is a necessary condition for the EVT to apply to a function?

• The function must have no critical points.

• The function must be continuous on a closed interval.

• The function must be linear.

• The function must be differentiable on an open interval.

How can you find the critical values of a function?

• By setting the function equal to zero.

• By finding where the derivative is zero or undefined.

• By evaluating the function at the endpoints.

• By checking the continuity of the function.

Why is it important to check if critical values are within the given interval?

• Because critical values outside the interval are always maxima.

• Because critical values within the interval are always minima.

• Because critical values outside the interval are irrelevant for finding extrema.

• Because critical values determine the continuity of the function.

Where can the extrema of a function occur?

• Only at points where the function is undefined.

• At the endpoints and critical values within the interval.

• Only at the critical values within the interval.

• Only at the endpoints of the interval.

What is the maximum value of the function on the interval [-1, 2]?

• 0

• 15

• 3

• -48

What is the minimum value of the function on the interval [-1, 2]?

• 3

• -48

• 15

• 0

Why is it important to write mathematical solutions in complete sentences?

• To make the solution longer.

• To ensure clarity and understanding for others reviewing the work.

• To avoid using mathematical symbols.

• To confuse the reader.