# Thread: Domain and largest/smallest integer

1. ## Domain and largest/smallest integer

I don't quite understand the problem when they ask for the smallest/largest integer in the domain of a function. Am I supposed to take the limit or something?
For example:
Find the smallest positive integer in the domain of f(x):
$f(x) = \frac{\sin^2x}{\sqrt{x^2-28x-29}}$
Do I take the derivative and find where it's decreasing?

and for this one:
Given $f(x) = x^2 - 27x - 28$, find the largest integer in which $f$ is decreasing.
So I found the derivative, did the sign chart and found that it was decreasing at 13.5. Is this right?

and for this one:
$f(x) = \frac{\sqrt{19x - x^2 - 34}}{e^x}$ has a domain of $[a,b]$. Find $b-a$
So for this one, I found the zero of the top of the fraction, which was 17 and 2, and I made those two the domain, so 17-2 = 15. Is this correct?

2. Originally Posted by steveo0
I don't quite understand the problem when they ask for the smallest/largest integer in the domain of a function. Am I supposed to take the limit or something?
no ... just determine the domain.
For example:
Find the smallest positive integer in the domain of f(x):
$f(x) = \frac{\sin^2x}{\sqrt{x^2-28x-29}}$

x^2 - 28x - 29 > 0
(x - 29)(x + 1) > 0

x > 29 ... x < -1

so ... what is the smallest positive integer in the domain?

and for this one:
Given $f(x) = x^2 - 27x - 28$, find the largest integer in which $f$ is decreasing.
So I found the derivative, did the sign chart and found that it was decreasing at 13.5. Is this right?

largest integer? wouldn't that be 13?

and for this one:
$f(x) = \frac{\sqrt{19x - x^2 - 34}}{e^x}$ has a domain of $[a,b]$. Find $b-a$
So for this one, I found the zero of the top of the fraction, which was 17 and 2, and I made those two the domain, so 17-2 = 15. Is this correct?

correct
help any?