Question

When finding absolute min and absolute max, which points do you plug in to f(x)?

a) Critical points
b) Inflection points
c) Endpoints of the interval
d) All of the above

Answer 1

To find the absolute min and max of a function, evaluate the function at critical points and the endpoints of the interval. Inflection points do not necessarily correspond to absolute extrema and are not required for this process. Option a, c.

Step-by-step explanation:

When finding the absolute minimum and absolute maximum values of a function f(x) on a closed interval, you should evaluate the function at the following points:

Critical points where the function's derivative is zero or undefined within the interval.

Endpoints of the interval, as these could potentially be the locations of absolute extrema.

Inflection points, where the second derivative is zero or undefined, do not necessarily correspond to absolute minimum or maximum values.

It is not required to plug in inflection points when only seeking absolute extrema. Instead, they are more relevant when analyzing the concavity of the curve and determining the intervals where the function is concave up or down.

So option a, c.