How do you find the linearization at (3,5,1) of # f(x,y,z) = sqrt(x^2 y^2 z^2)#?

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Answer 1 · 2016-09-23T08:06:36

#vec l(s) = s ((3),(5),(1))#

#nabla f = ((f_x),( f_y),( f_z)) = 1/sqrt(x^2y^2z^2) ((x),( y),( z))#

so a tangent vector is #((3),(5),(1))#

and the parameterised tangent line :

#vec l(s) = vec l_0 + s vec d#

is

#vec l(s) = ((3),(5),(1)) + s ((3),(5),(1))#

# = ((3),(5),(1))(s+1)#

# = ((3),(5),(1))s'#