Question

The temperature in degrees celsius on the surface of a metal plate is given by t(x, y), where x and y are measured in centimeters. find the direction from point p where the temperature increases most rapidly. t(x, y) = 45 − x2 − 2y2, p(1, −3)

Answer 1

Hello,

This is very old for me!


`dt= (\partial t)/(\partial x) *dx+ (\partial t)/(\partial y) *dy=0\\ =-2x*dx-4y*dy\\ \Rightarrow (dy)/(dx)=- (x)/(2y) \\ At\ P(1,-3)\ \\\\ \boxed{m=-(1)/(6)}`