Which approach helps organize potential extrema by listing end points and critical points and comparing their y-values?

Which approach helps organize potential extrema by listing end points and critical points and comparing their y-values?

• A. Create a table of end points and critical points and compare values.
• B. Only evaluate endpoints.
• C. Only differentiate and solve.
• D. Only evaluate interior points.

Answer: (D)

To locate extrema, you need to consider all potential candidates for where extrema could occur: interior points where the derivative is zero or undefined (critical points) and the endpoints of the domain. Evaluating the function at each of these x-values and comparing the resulting y-values tells you where the largest and smallest values occur. If you only look at interior points, you can miss an extreme that happens at an endpoint. If you only check endpoints, you might miss interior extrema indicated by where the derivative vanishes or fails to exist. By listing both endpoints together with all critical points and then comparing the corresponding y-values, you capture every possible extremum and identify the actual maximum and minimum.

To locate extrema, you need to consider all potential candidates for where extrema could occur: interior points where the derivative is zero or undefined (critical points) and the endpoints of the domain. Evaluating the function at each of these x-values and comparing the resulting y-values tells you where the largest and smallest values occur.

If you only look at interior points, you can miss an extreme that happens at an endpoint. If you only check endpoints, you might miss interior extrema indicated by where the derivative vanishes or fails to exist. By listing both endpoints together with all critical points and then comparing the corresponding y-values, you capture every possible extremum and identify the actual maximum and minimum.