Question
Approximating Critical Numbers In Exercises $7-10$ , approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown.graph can't copy
Approximating Critical Numbers In Exercises $7-10$ , approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. graph can't copy
Answers
Approximating Critical Numbers In Exercises $7-10$ , approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown.
graph can't copy
Our goal in this question is to approximate absolute or relative maximum and minimum on the following function shown. Do the interval through the open animal. Negative 1 to 1. So we compressed. Try and see if we have an absolute minimum and we could see it's gonna be somewhere near X equals negative one. Since this is where the function is that it's Lois. However, we cannot pinpoint an exact value due to the fact that this interval is open because the smallest value it can get without actually touching negative one is has infinite possibilities. It could be negative. 0.9 negative 0.99 Negatives. You're a 0.99999999 and those nines could go on forever. So because of this, we cannot say there's an absolute minimum at X. That's a point close to X equals negative one. So there is no we can see that this same principle applies at the point X equals one, since once again it's an open interval. So we can't even approximate in absolute max due to the fact that we will keep inching closer and closer to the end of interval but never actually quite touch it. Now we should check for a relative maxim enema so you can see that this function is increasing continuously. There's no, um, Ben's in this function, really, there is one X equals zero, which we can see is a critical point. However, this is not any max or men, since it's simply in between a lower point in the higher point. A relative maxim unusually has a curved shape something like this, which would be an absolute mint or something like this, which would be an absolute mix. So because of this, we can't say that there any relative or absolute maximum un dysfunction due to the fact that it's on an open inedible so there are no extreme for this function. I know this is only because it is on an open interval. Otherwise, the points X equals negative one and one would have been an absolute maximum on a closed interval
In this problem, we're given a graph of function and where Esther Works made the critical points. As you can see from 0 to 1, that dysfunction peaks. It is increasing and after this point it stars decreasing. And also, if you were to draw on present a line, it could be tension to function. For me, that exit goes toward the secret. A point. Now hear that solution for want to do The function is decreasing and from 2 to 3 is fortunate increasing so it changes behavior. It makes this point execution. The other good school point. Now between 200 feet dysfunction is increasing between PM or it is increasing again and change behavior does. It is a critical point, too, so well said at once is good for everyone except you get to read. The function, as you can see, is at its maximum. Also, consider this is local or the global maximum, and what X is equal to chew. It is it's meet him
We can see on this craft that we have to label the critical values and identify if it's an absolute or relative minimum. Max. So on this crap, we only have one critical value right at this point here. And you can see that because this is the only part where we can draw a stranger line that's completely yours on top or have your a slope. So we have to label this point so we can see that this will be an absolute max due to the fact that it is the, uh at this point has the highest. Why value? So on this one will have one point. That's an absolute max.
So for this problem, F is continuous but does not have any local minimums or maximums, but two and four are critical points. So if we're to draw something like that, it would look with this. So where to in that Ford? It looks like the functions about to level off when that keeps increasing again. And same thing with that four. It's about to level off within a keeps increasing again After four. These are what we call saddle, please.