Second Partial Derivatives in Parametric Equations Polar Coordinates  Rectangular Coordinates  Contents

Given a vector X(u,v)=(x(u,v),y(u,v),z(u,v)) we define the second partial derivatives componentwise as X_uv(u,v)=(x_uv(u,v),y_uv(u,v),z_uv(u,v))



[D]

Constrained Maxima and Minima Polar Coordinates  Rectangular Coordinates  Top of Page  Contents

If g(t) = X(u(t),v(t))⋅U for some non-zero vector U then z'(t)= X'(u(t),v(t)⋅U so z has a critical point if X'(u(t),v(t))=0 or if X'(u(t),v(t)) is perpendicular to U.



[D]