A function assigns the value. The function on which the extreme value theorem can be applied is f(x)=x/(x-6)².
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
In a function for the extreme value theorem to be applicable, the function must be continue between the given interval.
The denominator of the first function will not continue when the value of x= 6, which is not in the interval [3,5). Therefore, the extreme value theorem is applicable.
To verify if the system will continue or not, you can plot the graph of the function, and look between the interval if the function continues or not. As shown below.
Hence, the function on which the extreme value theorem can be applied is f(x)=x/(x-6)².
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