Erre az egyetemi lináris közelítéses matek feladatra mi a megoldás?

f(x,y) = x√y

a linearis kozelites a (8,81) pontban:

f(8,81) + df/dx(8,81)*(x-8) + df/dy(8,81)*(y-81)

df/dx = √y

df/dy = x/2√y

f(8,81) = 8*√81 = 72

df/dx(8,81) = √81=9

df/dy(8,81) = 8/2√81 = 4/9

A linearis kozelites tehat:

l(x,y) = 72 + 9*(x-8) + (4/9)*(y-81)

l(x,y) = 9x + (4/9)y - 36