Question

Please help me solve the following problem. Find a unit vector u that is normal at P(1,-2) to the level curve of f(x,y)=4(x^2)y through P.

Answer 1

\[f(x,y)=4x ^{2}y\]

Answer 2

FIND THE GRADIENT AND DEVIDE IT BY IT MODULE AT P

Answer 3

ok the gradient is:
\[(8xy)i+(4x ^{2})j\]

Answer 4

and divide by the magnitude at the point P?

Answer 5

at P it is (-16,4)
so unit vector is: (-16,4)/(sqrt{16^2+4^2))

Answer 6

you could. But since it is a level function you can get it faster by gradient. Sincé you know that it is always perpendicular to level curves

Answer 7

gradient vector is perpendicular to any level curve !!!