A path r(t) (x(t), y(t)) follows the gradient of a function (x, y) if the tangent vector r '(t) points in the direction of for all t In other words, r '(t) k(t) r(t) for some positive function k(t) In this case, r(t) crosses each level curve of (x, y) at a right angle Show that if the path r(t) (x(...

Since rt follows the gradient of fx y we ...

A path r(t) = (x(t), y(t)) follows the gradient of a function (x, y) if the tangent

Question:

A path r(t) = (x(t), y(t)) follows the gradient of a function ƒ(x, y) if the tangent vector r'(t) points in the direction of ∇ƒ for all t. In other words, r'(t) = k(t)∇ƒ_r(t) for some positive function k(t). In this case, r(t) crosses each level curve of ƒ(x, y) at a right angle.

Show that if the path r(t) = (x(t), y(t)) follows the gradient of ƒ(x, y), then

(1), A F = x' (t) fx