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

Assume that the surface temperature distribution of an ellipsoid shaped object given by 4x^{2}+ y^{2}+ 4z^{2}= 16 is T(x,y,z) = 8x^{2}+ 4yz - 16z + 600.

2. Relevant equations

3. The attempt at a solution

I'm assuming we just have to find the maximum value of this function using the lagrange method.

I started by writing the equation like this:

8x^{2}+ 4yz -16z + 600 - 4x^{2}[tex]\lambda[/tex] - y^{2}[tex]\lambda[/tex] - 4z^{2}[tex]\lambda[/tex] + 16[tex]\lambda[/tex].

Then I found the 4 partials and set them to 0:

f_{x}= 16x - 8x[tex]\lambda[/tex] = 0

f_{y}= 4z - 2y[tex]\lambda[/tex] = 0

f_{z}= 4y - 16 - 8z[tex]\lambda[/tex] = 0

f_{[tex]\lambda[/tex]}= -4x^{2}- y^{2}- 4z^{2}+ 16 = 0

My problem comes next when I try to solve this system of equations.

When I solve them I get:

x = 1 (or 0?)

y = z = -(4/3)

[tex]\lambda[/tex] = 2

These don't check out.

Does it looks like I'm going about this problem correctly? If so what am I doing wrong when solving the system of equations?

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# Lagrange multipliers

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