Question

I messed up :(

suppose we have a function on the interval [0,3]
and we want to determine where the function is increasing and decreasing , and our critical numbers were 2 and 4

what I did it since 4 is not on the interval i put 0 and 3 and took numbers greater than 3 and smaller than 0 and between 0 and 3 :(

what is the correct way ?

should I put only 2 ?
if I did , the function would be increasing all the time , so there will be no absolute max , but there was an absolute max and min.

Answer 1

check 0 2 and 3 as critical values

Answer 2

I know , the question was on two parts , part one asks for the absolute max,mid , and there was a large value and a small value , so the largest was the max and the smallest was the min,

but on part 2 , he asks for where the functions increasing and decreasing ,

if I put 2 the function would be increasing so there will be no absolute max , what should I put on the numbers line ?

Answer 3

so you are only suppose to be looking from 0 to 3 and the only critical number you have between there is 2.
You test 0 to 2 and also 2 to 3.

Answer 4

You have two intervals to test on [0,3] in other words.

Answer 5

but the function at this point would be increasing all the time , so there will be no absolute max , but I've found the absolute max

Answer 6

so if I took numbers larger than 2 the function would be increasing , and I i found numbers smaller than 2 the function will also be increasing.

Answer 7

and if I took numbers smaller than 2 **

Answer 8

You will have absolute max at the highest point
You will have absolute min at the lowest point
There will be a highest and lowest point since you are only looking from 0 to 3 (we know our function will not be going on forever)

Answer 9

what I've learned is when the function get to negative when we take numbers smaller or greater the function is decreasing , and if we took numbers smaller or greater and it we got a positive answer , the function is then increasing.

the function when I took 1 were positive , and when I took 2.5 and 3 it was also positive.

Answer 10

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you may have something like this



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