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Find the local minimum value of f(t,v) =ITV:...

Question

Find the local minimum value of f(t,v) =ITV:

Find the local minimum value of f(t,v) = ITV:



Answers

Find all local maximum and minimum values of the function whose graph is shown.

All right, let's talk about maximum and minimum. Okay, so suppose that we have a point. See? Okay. And this point, c has to be an interior point within a certain interval. Okay? Now, if the Y value of that interior point is greater than or equal to the points around it, we call it a maximum. Okay, So if FFC or the Y value of that C is greater than or equal to f of X or the points that surrounding it, we call that a local maximum. Now, if the Y value or FFC of that interior point is less than or equal to the points that are around the Y values that are around it, then we call that a local minimum. All right, so now let's look at a slight graph. And of course, this graph is not going to be drawn to scale. It's just something Teoh give you a picture to refer to. Okay, so we're gonna be on a interval from a to be all right. And let's say we have a graph that starts here, comes down, comes back up, goes slightly down and then comes back up here. All right. Now, remember that our point C order for it to be a local maximum and minimum. It has to be an interior point. So this points over here at a excuse me. These points over here at B would not matter. And these points over here a would not matter because those are not interior points. However, let's say this point right here is de We have this point here which is E in this point here, which is F and of course, this is not drawn to scale. Remember that this is not drawn to scale. Okay, so because this point d right here is below, we call that a local minimum. We also have another local minimum down here at s and says this point interior point here is above We call that a local maximum. Okay, Now, if the question is asked you what your maximum values, the maximum value is always f of sea or the y value, whereas the actual maximum itself is always gonna be at whatever X is so we can say right in. For example, in our case is going to be X is equal to D

Okay, So if we have applied at seeing for are greater than or equal to off of X for all ex contained in an open interval. I This is an open interval. Ah, it contains See and FFC is a local next Ah us. And now if we have f of C is less than or equal to affect for us containing iis an opening interval then we know that FFC is a local men.

We have to list the local minimum values for the function if from the graph. So as we can see that F takes a local minimum at minus 80 on at five. So F takes a local minimum value at minus 80 and five such that f at minus eight is equal toe minus four. F at zero is equal to zero on F at five is also equal to zero.

Okay, So here's the graph of X cubed. It's ah pretty basic, one that most people know how to graph. If not, you can plot a couple points and easily find it, and we're supposed find the max is in the minimums. And so if we're looking at this, that Max is kind of like the heisted ever goes. But since it just goes like, straight up over here and it keeps going up, this actually has no Max is because it just keeps going up to infinity and you can really count. Infinity is a max and similar airily, right? If it's down there, you're not gonna have any minimums. So this actually has no maxes or no minimums rights. You can say this like overall has none if you need to. Um, but that's just bleep. Basically, it doesn't have any local maximum because there's no kind of like humps in it, right? If it kind of homes and then went back up and hump, if it had something like that, I could say, Hey, it's local. It's not over absolutely coverall, but this doesn't even have any of that. It just goes kind of one direction. It's continually getting bigger in both the positive and negative directions. So no Max's Normans


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