Question 1207693: Find a and b.
If 2 < x < 4, then a < 1/(x - 6) < b.
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
2 < x < 4
Substitute the greatest lower bound of x, which is 2 1/(2-6) = -1/4
and the least upper bound of x, which is 4. 1/(4-6) = -1/2
Since 1/(x-6) is continuous and decreasing for x < 6, it's approaching -1/2 from
below as x approaches 4 from the left, and approaching -1/4 as x approaches 2
from the right,
-1/2 < 1/(x - 6) < -1/4
Edwin
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
On the given interval 2 < x < 4, the function 1/(x-6) is monotonic, so the maximum and minimum values of the function on that interval are at the endpoints of the interval.
x=2; 1/(x-6)=1/(-4)=-1/4
x=4; 1/(x-6)=1/(-2)=-1/2
Note that the function value is less ("more negative") at x=4, so the function value at x=4 is the lower end of the range of function values.
ANSWER: a=-1/2,b=-1/4;
i.e., -1/2 < 1/(x-6) < -1/4
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