1. ## Maximum value

Why does: n/(n+k) have a maximum value of 1 for k = 0, and for no other values of k?

2. Originally Posted by Aquafina
Why does: n/(n+k) have a maximum value of 1 for k = 0, and for no other values of k?
Hi

n being fixed, as k increases, (n+k) increases, 1/(n+k) decreases, n/(n+k) decreases
The maximum value is therefore obtained for k=0

3. Now if n were fixed, like my friend runnig gag says, with k being a variable. this function has no limit as to how high it will go.

When the denominator (n+k) aproaches zero, The function grows without bound and therefore has no maximum height.

Is n fixed or not? Because this would change things a bit.

4. ## no max.

considering it be a function of k,

its a rectangular hyperbola,

we have an asymptote at k=-n,

so there is basically no max. (it goes up to infinity)

5. thanks..

in reply to the first post, how is k=0 the maximum value the expression is decreasing for 1/n+k and n/n+k like you said?

and with the rectangular hyperbole, so that would imply no maximum value? i.e. it is minus infinity? but we assuming k is = to or > 0 so we take 0?

6. k=0 is not the max value.

and the rectangular hyperbola(y=1/x) looks like so:

your would just shift left/right as per the transformation. so the max/min values remain the same.

it takes all values between -infinity to +infinity

7. Hey, that's what i said!

8. Originally Posted by VonNemo19
Hey, that's what i said!
??

9. hi, thank, no n is not fixed, it is basically a probability:

n = number of balls
k = how many balls are withdrawn from a bag

and in a particular situation the probability comes out to: n/n+k