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Hello, my name is christina and in this video we will determine the linearization of a given function in three variables at three different given points.
00:14
In our case, this is fxy z, and our three points are 111, 100, and 0 ,000.
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For each of this cases, we will need the first derivatives in each respective variable.
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So let's start with that.
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First derivative respect to y is x plus z.
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And first derivative of the function of respect to z is y plus x.
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And now for each case, we'll calculate the values in each point and apply the definition as seen here.
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So for a, f in 1, 1, 1 is 3, fx in the same point, is 2, first derivative respect to y and 1 -1 is 2, and z 1 -1 is also 2.
01:44
Now we apply the definition l x -y -z, we get 3 plus 2, x minus 1, plus 2, 1 minus 1, plus 2 times z minus 1...