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!

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