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Are the statements true or false? Give reasons for your answer.Every function has a global maximum....

Question

Are the statements true or false? Give reasons for your answer.Every function has a global maximum.

Are the statements true or false? Give reasons for your answer. Every function has a global maximum.



Answers

True or False If $f(c)$ is a local maximum of a continuous function $f$ on an open interval $(a, b),$ then $f^{\prime}(c)=0 .$ Justify your answer.

We'll see how this Halloween, therefore in question, Uh, I have a quick D's continues function Horned clothes Interval. Go see that thing? You know, a little more on DA All the reasoning is it's pretty straight for So you haven't seen inflection The closing of Also See, There you have it on the interval From a to be see these continues. Oh, well, there's gonna be used to find that a I love the series continues. He's just, uh whatever you presented us, so function joining those two points back continues line. So Well, was he was he here? You know something? No marks on one of the point I'm little somethings that mean Well, but younger. But yes, you does on, uh, well, the recent enemies, huh? All the the extreme value theorem. Yeah. All right. Jeez. Guarantees? No, but they are good hypothesis. Yeah, a quick demonstration is a close interval. So in this case would be honor and be on the four more extreme cases. Like state of you. What? Uh, something that a racism, Uh, but all he's Ah, can we really? So much Because it has to go back to the much of the point, Billy. Hey. Be so the reason is you didn't close Interval and you're doing a continuous line. You have a thing so remarkable, boring Tillman so much about you, Toe. So that's it? He's, uh yes, it does. Yeah.

It's clear. So we knew right here. So we have a statement. A function is always 1 to 1. So let's let me have half of X is equal to X square, which is not 1 to 1 because of one is equal to one square, which is equal to one which is also equal to a negative one, so we know that it's false.

Okay, The given statement is true, and the reason why is if you continue if you consider a continuous function on a closed interval. If you know the F is not bounded on the interval, then you know there's a value see on the interval a comma. Be such that increases or decreases without bound when X approaches this value seat. Therefore, we know that we're the limit is approaching positive infinity from sea to the right and from sea to the left. So there's a vertical ask himto at X equal see which contradicts the continuity of f of X. So there is one real value that minimizes or maximizes the function. Therefore, this

All right, consider the function. Why is equal to X squared, right? So this has the shape for the the part of the function. Looks like this here. Right. So we know that this is a continuous and nonlinear function, right? So it is continuous and non linear. Right? But this does not have a maximum, right? It goes off to positive infinity. Right? So there is no maximum. So this is an example where we have a continuous and nonlinear function with no maximum. So this statement is false.


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