Answer:
Step-by-step explanation:
1) f(x) = x+y , xy = 49 --> f(x) = x+49/x
f '(x) = 1-49/x2 , x = ±√49 , choose x = +7
y = 49/x = 7
smaller = 7
larger = 7
2) Vertical Distance is difference between the two functions
V(x) = x+56 - x2, V '(x) = 1 -2x --> x = 1/2 --> V(1/2) = 56.25 <---Max Vertical distance
Boundary at -7 and 8 are less
3) I googled the equation, it is really y(n) = kn/(49+n2)
y '(n) = (k(49+n2) - 2kn2)/(49+n2) , Setting to zero, k(49+n2) -2kn2 = 0 , n = 7
4) Let x and y be the sides of the rectangle. A = xy = 37.5 Million or y = 37.5/x
The length of the fences is f(x) = 2x + 3y = 2x+112.5/x
f '(x) = 2-112.5/x2 --> x = √56.5 = 7.5 and y = 37.5/7.5 = 5 then scale by √Million
smaller = 5000 ft and larger = 7500 ft
this took me ages to work out so hopefully it helped
![x \sqrt[3]{ \frac{6}{x}}](https://tex.z-dn.net/?f=%20x%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B6%7D%7Bx%7D%7D%20)
![\frac{6x}{ \sqrt[3]{36x}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6x%7D%7B%20%5Csqrt%5B3%5D%7B36x%7D%7D%20)