Find the maximum and minimum values of f(x, y,z)=5x+4y+1z on the sphere x2+y2+z2=1.

Use Lagrange multipliers. The Lagrangian is



with partial derivatives (set equal to 0)






We can substitute the first three equations into the fourth to solve for :




Now use these values of to solve for , which should give you two critical points at , which would respectively give a maximum and minimum value of .

Ithink its 126 hope its

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