Final answer:
To find the absolute maximum and minimum on an interval, you can use methods such as critical points, the endpoint method, evaluating at inflection points, and calculating the average rate of change.
Step-by-step explanation:
When finding the absolute maximum and minimum on an interval, there are several methods you can use:
a) Use critical points: Find the critical points of the function within the interval by taking the derivative and setting it equal to zero. Check the values at the critical points and endpoints to determine the absolute maximum and minimum.
b) Apply the endpoint method: Evaluate the function at the endpoints of the interval and compare the values to determine the absolute maximum and minimum.
c) Evaluate at inflection points: If there are any inflection points within the interval, evaluate the function at those points to see if they are absolute maximum or minimum.
d) Calculate the average rate of change: Find the average rate of change of the function over the interval and compare it to the values at the critical points and endpoints to determine the absolute maximum and minimum.