The answer is B. The values of y must only be positive because it is equal to
![| - x|](https://tex.z-dn.net/?f=%20%7C%20-%20x%7C%20)
The other options states that the values of y could be negative which is why it is wrong.
To find t<span>he relative maximum value of the function we need to find where the function has its first derivative equal to 0.
Its first derivative is -7*(2x)/(x^2+5)^2
</span>7*(2x)/(x^2+5)^2 =0 the numerator needs to be eqaul to 0
2x=0
x=0
g(0) = 7/5
The <span>relative maximum value is at the point (0, 7/5).</span>
We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (<span>Triangle Inequality Theorem)
so
inequality 1
</span>
![(2+7) \ \textgreater \ x \\ 9 \ \textgreater \ x \\ x \ \textless \ 9 in](https://tex.z-dn.net/?f=%282%2B7%29%20%5C%20%5Ctextgreater%20%5C%20%20x%20%5C%5C%20%209%20%5C%20%5Ctextgreater%20%5C%20%20x%20%5C%5C%20%20x%20%5C%20%5Ctextless%20%5C%20%209%20in%20)
<span>
inequality 2
</span>
![(x+2) \ \textgreater \ 7 \\ x \ \textgreater \ 7-2 \\ x \ \textgreater \ 5 in](https://tex.z-dn.net/?f=%28x%2B2%29%20%5C%20%5Ctextgreater%20%5C%20%207%20%5C%5C%20%20x%20%5C%20%5Ctextgreater%20%5C%20%207-2%20%5C%5C%20%20x%20%5C%20%5Ctextgreater%20%5C%20%205%20in%20)
<span>
the answer is
</span>
![5 in \ \textless \ x \ \textless \ 9 in](https://tex.z-dn.net/?f=5%20in%20%20%5C%20%5Ctextless%20%5C%20x%20%5C%20%5Ctextless%20%5C%209%20in)
<span>
</span>
4-1.175=2.825
There was 2.825 liters left in the tank.
Hope this helps.