Determine if EVT applies (Calculus I)

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In summary, the Extreme Value Theorem states that if a function is continuous on a closed interval, it will have an absolute maximum and minimum value within that interval. In the given problem, since the function is continuous on the interval [2, 8] and -4 is not within that interval, the EVT should apply.
  • #1
Blablablabla
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Homework Statement


Determine if the EVT (Extreme Value Theorem) applies to the following.

Untitled.png


on the interval [2, 8]

The Attempt at a Solution



For the Extreme Value Theorem to apply, the function must be on an interval, and the function must be continious.

I believe the domain for this function is {x | x ≠ -4}

But since -4 is not in the interval, the EVT should apply.
 
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  • #2
Blablablabla said:

Homework Statement


Determine if the EVT applies to the following.

http://www4a.wolframalpha.com/Calculate/MSP/MSP8951a40h06a29428ad200001gbeeg8268c71ecc?MSPStoreType=image/gif&s=59&w=100&h=39 [Broken]

on the interval [2, 8]



The Attempt at a Solution



For the EVT to apply, the function must be on an interval, and the function must be continious.

I believe the domain for this function is {x | x ≠ -4}

But since -4 is not in the interval, the EVT should apply.

(1) What on Earth is an EVT?
(2) Image does not show up on screen.

RGV
 
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  • #3
Hi, sorry about that. I fixed it
 
  • #4
Blablablabla said:
Hi, sorry about that. I fixed it

What, exactly, does the EVT say? I mean the version of the EVT theorem in your textbook or course notes. (I have seen some versions in which the answer would be "no" and other versions in which the answer would be "yes".)

RGV
 
  • #5
The Extreme Value Theorem

If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f(c) for some number c in [a, b] and an absolute minimum value f(d) for some number d in [a, b].

That's what my textbook says
 

1. What is EVT?

EVT stands for the Extreme Value Theorem. It is a theorem in calculus that states that a continuous function on a closed interval must have a maximum and minimum value within that interval.

2. How do I determine if EVT applies to a function?

To determine if EVT applies, you must first check if the function is continuous on the interval in question. If it is continuous, then you must also check if the interval is closed. If both of these conditions are met, then EVT applies to the function.

3. What does it mean if EVT applies to a function?

If EVT applies to a function, it means that the function must have a maximum and minimum value within the given interval. This can be useful in finding the maximum and minimum values of a function, as well as in proving the existence of these values.

4. Can EVT be applied to all functions?

No, EVT can only be applied to continuous functions on a closed interval. If a function is not continuous or the interval is not closed, then EVT does not apply.

5. How is EVT used in calculus?

EVT is used in calculus to find the maximum and minimum values of a function on a given interval. It is also used in proving the existence of these values and in solving optimization problems.

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