(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A heat-seeking missile is located at (2,-3) on a plane. The temperature function is

given by T(x; y) = 20-4x^2-y^2. Find the equation of the curve along which the

missile travels, if it continuously moves in the direction of maximum temperature

increase. Express your answer in the form x = f(y). Show the calculations.

2. Relevant equations

T(x; y) = 20-4x^2-y^2

3. The attempt at a solution

I know the missile will travel along the direction of the gradient. The gradient with respect to x is -8x and the gradient with respect to y is -2y. The problem I'm having is getting the equation in terms of x. My only idea is to take δx(2,-3)(x-2)+δy(2,-3)(y+3)=0 and solve for x where x and δy are the gradients with respect to x and y. Is that correct?

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# Homework Help: Equation of a curve in 3 dimensions

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