First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is

. Set the derivative equal to 0 and factor to find the critical numbers.

, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.
X=2 is the answer to your question
Answer:
f(x)=11.1035−0.920848x
Step-by-step explanation:
Answer:

Step-by-step explanation:
First we have to write down what it says in the question in as an expression. So we know that there is already 3 people on Britany's team (herself and the two friends), that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. So....
Let "x" be the number of people who decided to join Britany and her friends
Let "y" be the total number of people on Britanie's team, then .....
3 + x = y
Now we need to remember that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. We can write that down as......

Now from this we know that the minimum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 9. The maximum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 15. And so we get.....
Minimum value:
3 + x = 9
x = 9 -3
x = 6
Maximum value:
3 + x = 15
x = 15 - 3
x = 12
Now we know that x will be equal to any integer between 6 and 12 so
