Understanding Absolute Extrema

What does the Extreme Value Theorem guarantee for a continuous function on a closed interval?

• It guarantees the function will have a derivative.

• It guarantees the function will have a maximum and a minimum.

• It guarantees the function will be differentiable.

• It guarantees the function will be linear.

What is the first step in finding the absolute extrema of a function on a closed interval?

• Evaluate the function at the endpoints.

• Find the critical points of the function.

• Check if the function is linear.

• Determine if the function is differentiable.

How do you find critical points of a function?

• By evaluating the function at the endpoints.

• By finding where the first derivative is zero or undefined.

• By checking if the function is continuous.

• By setting the second derivative to zero.

What is the next step after finding the critical points of a function?

• Check if the critical points are within the interval.

• Find the second derivative.

• Evaluate the function at each critical point and endpoint.

• Compare the critical points.

How do you determine the absolute maximum and minimum of a function?

• By evaluating the second derivative.

• By checking the continuity of the function.

• By comparing the y-values at critical points and endpoints.

• By finding the highest and lowest x-values.