- #1
sdevoe
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Homework Statement
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.
Homework Equations
T(x; y) = 20-4x^2-y^2
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?