Locating extrema Consider the graph of a function ƒ on the int...

Question

Locating extrema Consider the graph of a function ƒ on the interval [-3, 3].

b. Give the approximate coordinates of the absolute maximum and minimum values of ƒ (if they exist).

Accepted Answer

Hello. In this video, we are going to be identifying the values of X that represent an absolute minimum and absolute maximum value. So, the problem tells us that we are given a function F of X defined on the interval from -3 to 5.5. Which of the following X values represents an absolute minimum and maximum value of F of X? To start this problem, let's go ahead and identify the values of X. They are an absolute maximum. Now, what does it mean to be an absolute maximum of a graph? The absolute maximum value. Is the portion of the graph that has the largest possible y value. If we are taking a look at the graph given to us, the highest point along the defined interval that the graph reaches is located at the very end point of the graph. At this end point, we have the value X is equal to 5.5. Since this is the highest possible value that the graph reaches, this value of X is going to be the absolute maximum. So, we have an absolute maximum located at the X value 5.5. Now, what about the absolute minimum? While the absolute minimum is the opposite characteristic to the absolute maximum. The absolute minimum is the lowest possible value that the graph reaches on the defined interval. Now, if we take a look at the leftmost endpoint, the lowest possible value that this graph has is located at the value X is equal to -3. But notice that also along this y value of -9, we have another point of the graph that reaches the Y value -9. That is also at the X value, X is equal to 3. What this means is that there are two values of X that are considered to be absolute minimums. Those values of X are going to be positive and negative 3 on the X axis. With that being said, this is going to be the solution to this problem. The absolute minimum is located at positive and negative 3, and the absolute maximums are located at 5.5. So I hope this video helps you in understanding how to identify these values, and I will go ahead and see you all in the next video.

Locating extrema Consider the graph of a function ƒ on the interval [-3, 3]. <IMAGE>
b. Give the approximate coordinates of the absolute maximum and minimum values of ƒ (if they exist).

Watch next

Locating extrema Consider the graph of a function ƒ on the interval [-3, 3]. <IMAGE>b. Give the approximate coordinates of the absolute maximum and minimum values of ƒ (if they exist).

Watch next

Locating extrema Consider the graph of a function ƒ on the interval [-3, 3]. <IMAGE>
b. Give the approximate coordinates of the absolute maximum and minimum values of ƒ (if they exist).