If juliana and brody hiked both of the trails listed in the table, how far did they hike? 3 2/3 and 2 5/6

they both would've walked 6.5.

Implicit differntiation, yeah
remember
the deritivive of f(x)/g(x)=(f'(x)g(x)-g'(x)f(x))/(g(x)^2)

so

2x+2y(dy/dx)=0
minus 2x
2y(dy/dx)=-2x
divide both sides by 2y
dy/dx=-x/y

take derivitve again
(-x'y-y'x)/(y^2)
remember, y'=dy/dx=-x/y
(-y-(-x/y)x)/(y^2)
at (4,3)
at x=4 and y=3
(-3-(-4/3)4)/(3^2)=
(-3+16/3)/9=
(-9/3+16/3)/9=
(7/3)/9=
7/27
the value is 7/27
it is concave up at that point btw