Question

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=4x+3y+4z, subject to the constraint x^2+y^2+z^2=16, if such values exist.

Answer 1

I got a max of 160/sqrt(41) at point (12/sqrt(41),16/sqrt(41),64/sqrt(41)
and a min of -160/sqrt(41) at point 160/sqrt(41) at point (-12/sqrt(41),-16/sqrt(41),-64/sqrt(41))

where did I go wrong?

Answer 2

@myininaya

Answer 3

find the gradient vectors for both the function and the constraint

Answer 4

did already.

Answer 5

put these values in the constraint