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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)

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caylus
Hello,

This is very old for me!

[tex]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}} [/tex]




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