Question

Determine the absolute maximum and minimum of a function graphed over the interval (-5, 4].

a) Critical points
b) Endpoints
c) Local extrema
d) Inflection points

Answer 1

To determine the absolute maximum and minimum of a function, we consider the critical points, endpoints, local extrema, and inflection points.

Step-by-step explanation:

To determine the absolute maximum and minimum of a function graphed over the interval (-5, 4], we need to consider the critical points, endpoints, local extrema, and inflection points. Let's go through each step:

1. First, find the critical points by finding the derivative of the function and setting it equal to zero. The values where the derivative is zero or undefined are the critical points.
2. Next, check the endpoints of the interval. Since the interval is (-5, 4], we need to evaluate the function at -5 and 4.
3. Then, find the local extrema by checking the values of the function at the critical points and the endpoints. The highest value will be the absolute maximum and the lowest value will be the absolute minimum.
4. Finally, check for inflection points by finding the second derivative of the function and checking if it changes sign.