Math Help - Urgent! Help.. Multivariable

1. 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

2. 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."

$\nabla T = \left( \frac{\partial T}{\partial x },\frac{\partial T}{\partial y} \right)$

3. And once you have that, your path must always have that vector as tangent vector so you must have $\frac{dx}{dt}= \frac{\partial T}{\partial x}$ 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.