Thread: Urgent! Help.. Multivariable

A particle is located at the point (2,-3) on a metal plate whose temperature at (x,y) is

T(x,y) = 100 - 4x^2 - y^2

Find the equation of the path (in terms of x and y) of the particle as it continuously moves in the direction of maximum temperature increase

Please help.. I can't seems to understand and solve the Qn

By definition of Gradient (Gradient - Wikipedia, the free encyclopedia)

"In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change."

And once you have that, your path must always have that vector as tangent vector so you must have and [tex]\frac{dy}{dt}= \frac{\partial T}{\partial y}[/quote].

Solving those two differential equations will give you x and y as functions of the parameter t.